How to find an angle with tangent - ACT Math

Card 0 of 45

Question

In the above triangle, and . Find $\theta$ .

Answer

With right triangles, we can use SOH CAH TOA to solve for unknown side lengths and angles. For this problem, we are given the opposite and adjacent sides of the triangle with relation to the angle. With this information, we can use the tangent function to find the angle.

$\tan = \frac{opposite}{adjacent}$

$\tan\left ( \theta\right ) = \frac{4}{7} = 0.57$

$\arctan\left ( 0.57\right ) = \theta$

$29.7^{\circ}= \theta$

Compare your answer with the correct one above

Question

For the above triangle, and . Find $\theta$ .

Answer

With right triangles, we can use SOH CAH TOA to solve for unknown side lengths and angles. For this problem, we are given the opposite and adjacent sides of the triangle with relation to the angle. With this information, we can use the tangent function to find the angle.

$\tan = \frac{opposite}{adjacent}$

$\tan\left ( \theta\right ) = \frac{21}{8} = 2.63$

$\arctan\left ( 2.63\right ) = \theta$

$69.1^{\circ}= \theta$

Compare your answer with the correct one above

Question

For the above triangle, and . Find $\theta$ .

Answer

With right triangles, we can use SOH CAH TOA to solve for unknown side lengths and angles. For this problem, we are given the opposite and adjacent sides of the triangle with relation to the angle. With this information, we can use the tangent function to find the angle.

$\tan = \frac{opposite}{adjacent}$

$\tan\left ( \theta\right ) = \frac{14}{28} = 0.5$

$\arctan\left (0.5\right ) = \theta$

$26.6^{\circ}= \theta$

Compare your answer with the correct one above

Question

A laser is placed at a distance of $47\textup{ feet}$ from the base of a building that is $23\textup{ feet}$ tall. What is the angle of the laser (presuming that it is at ground level) in order that it point at the top of the building?

Answer

You can draw your scenario using the following right triangle:

Recall that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side of the triangle. You can solve for the angle by using an inverse tangent function:

$\small \Theta = tan^-^1(\frac{23}{47})=26.07535558394878$ or $26.08$^{\circ}$$ .

Compare your answer with the correct one above

Question

What is the value of $\small \Theta$ in the right triangle above? Round to the nearest hundredth of a degree.

Answer

Recall that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side of the triangle. You can solve for the angle by using an inverse tangent function:

$\small \Theta = tan^-^1(\frac{45}{27})=59.03624346792652$ or $59.04$^{\circ}$$ .

Compare your answer with the correct one above

Question

In the above triangle, and . Find $\theta$ .

Answer

With right triangles, we can use SOH CAH TOA to solve for unknown side lengths and angles. For this problem, we are given the opposite and adjacent sides of the triangle with relation to the angle. With this information, we can use the tangent function to find the angle.

$\tan = \frac{opposite}{adjacent}$

$\tan\left ( \theta\right ) = \frac{4}{7} = 0.57$

$\arctan\left ( 0.57\right ) = \theta$

$29.7^{\circ}= \theta$

Compare your answer with the correct one above

Question

For the above triangle, and . Find $\theta$ .

Answer

With right triangles, we can use SOH CAH TOA to solve for unknown side lengths and angles. For this problem, we are given the opposite and adjacent sides of the triangle with relation to the angle. With this information, we can use the tangent function to find the angle.

$\tan = \frac{opposite}{adjacent}$

$\tan\left ( \theta\right ) = \frac{21}{8} = 2.63$

$\arctan\left ( 2.63\right ) = \theta$

$69.1^{\circ}= \theta$

Compare your answer with the correct one above

Question

For the above triangle, and . Find $\theta$ .

Answer

With right triangles, we can use SOH CAH TOA to solve for unknown side lengths and angles. For this problem, we are given the opposite and adjacent sides of the triangle with relation to the angle. With this information, we can use the tangent function to find the angle.

$\tan = \frac{opposite}{adjacent}$

$\tan\left ( \theta\right ) = \frac{14}{28} = 0.5$

$\arctan\left (0.5\right ) = \theta$

$26.6^{\circ}= \theta$

Compare your answer with the correct one above

Question

A laser is placed at a distance of $47\textup{ feet}$ from the base of a building that is $23\textup{ feet}$ tall. What is the angle of the laser (presuming that it is at ground level) in order that it point at the top of the building?

Answer

You can draw your scenario using the following right triangle:

Recall that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side of the triangle. You can solve for the angle by using an inverse tangent function:

$\small \Theta = tan^-^1(\frac{23}{47})=26.07535558394878$ or $26.08$^{\circ}$$ .

Compare your answer with the correct one above

Question

What is the value of $\small \Theta$ in the right triangle above? Round to the nearest hundredth of a degree.

Answer

Recall that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side of the triangle. You can solve for the angle by using an inverse tangent function:

$\small \Theta = tan^-^1(\frac{45}{27})=59.03624346792652$ or $59.04$^{\circ}$$ .

Compare your answer with the correct one above

Question

In the above triangle, and . Find $\theta$ .

Answer

With right triangles, we can use SOH CAH TOA to solve for unknown side lengths and angles. For this problem, we are given the opposite and adjacent sides of the triangle with relation to the angle. With this information, we can use the tangent function to find the angle.

$\tan = \frac{opposite}{adjacent}$

$\tan\left ( \theta\right ) = \frac{4}{7} = 0.57$

$\arctan\left ( 0.57\right ) = \theta$

$29.7^{\circ}= \theta$

Compare your answer with the correct one above

Question

For the above triangle, and . Find $\theta$ .

Answer

With right triangles, we can use SOH CAH TOA to solve for unknown side lengths and angles. For this problem, we are given the opposite and adjacent sides of the triangle with relation to the angle. With this information, we can use the tangent function to find the angle.

$\tan = \frac{opposite}{adjacent}$

$\tan\left ( \theta\right ) = \frac{21}{8} = 2.63$

$\arctan\left ( 2.63\right ) = \theta$

$69.1^{\circ}= \theta$

Compare your answer with the correct one above

Question

For the above triangle, and . Find $\theta$ .

Answer

With right triangles, we can use SOH CAH TOA to solve for unknown side lengths and angles. For this problem, we are given the opposite and adjacent sides of the triangle with relation to the angle. With this information, we can use the tangent function to find the angle.

$\tan = \frac{opposite}{adjacent}$

$\tan\left ( \theta\right ) = \frac{14}{28} = 0.5$

$\arctan\left (0.5\right ) = \theta$

$26.6^{\circ}= \theta$

Compare your answer with the correct one above

Question

A laser is placed at a distance of $47\textup{ feet}$ from the base of a building that is $23\textup{ feet}$ tall. What is the angle of the laser (presuming that it is at ground level) in order that it point at the top of the building?

Answer

You can draw your scenario using the following right triangle:

Recall that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side of the triangle. You can solve for the angle by using an inverse tangent function:

$\small \Theta = tan^-^1(\frac{23}{47})=26.07535558394878$ or $26.08$^{\circ}$$ .

Compare your answer with the correct one above

Question

What is the value of $\small \Theta$ in the right triangle above? Round to the nearest hundredth of a degree.

Answer

Recall that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side of the triangle. You can solve for the angle by using an inverse tangent function:

$\small \Theta = tan^-^1(\frac{45}{27})=59.03624346792652$ or $59.04$^{\circ}$$ .

Compare your answer with the correct one above

Question

In the above triangle, and . Find $\theta$ .

Answer

With right triangles, we can use SOH CAH TOA to solve for unknown side lengths and angles. For this problem, we are given the opposite and adjacent sides of the triangle with relation to the angle. With this information, we can use the tangent function to find the angle.

$\tan = \frac{opposite}{adjacent}$

$\tan\left ( \theta\right ) = \frac{4}{7} = 0.57$

$\arctan\left ( 0.57\right ) = \theta$

$29.7^{\circ}= \theta$

Compare your answer with the correct one above

Question

For the above triangle, and . Find $\theta$ .

Answer

With right triangles, we can use SOH CAH TOA to solve for unknown side lengths and angles. For this problem, we are given the opposite and adjacent sides of the triangle with relation to the angle. With this information, we can use the tangent function to find the angle.

$\tan = \frac{opposite}{adjacent}$

$\tan\left ( \theta\right ) = \frac{21}{8} = 2.63$

$\arctan\left ( 2.63\right ) = \theta$

$69.1^{\circ}= \theta$

Compare your answer with the correct one above

Question

For the above triangle, and . Find $\theta$ .

Answer

With right triangles, we can use SOH CAH TOA to solve for unknown side lengths and angles. For this problem, we are given the opposite and adjacent sides of the triangle with relation to the angle. With this information, we can use the tangent function to find the angle.

$\tan = \frac{opposite}{adjacent}$

$\tan\left ( \theta\right ) = \frac{14}{28} = 0.5$

$\arctan\left (0.5\right ) = \theta$

$26.6^{\circ}= \theta$

Compare your answer with the correct one above

Question

A laser is placed at a distance of $47\textup{ feet}$ from the base of a building that is $23\textup{ feet}$ tall. What is the angle of the laser (presuming that it is at ground level) in order that it point at the top of the building?

Answer

You can draw your scenario using the following right triangle:

Recall that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side of the triangle. You can solve for the angle by using an inverse tangent function:

$\small \Theta = tan^-^1(\frac{23}{47})=26.07535558394878$ or $26.08$^{\circ}$$ .

Compare your answer with the correct one above

Question

What is the value of $\small \Theta$ in the right triangle above? Round to the nearest hundredth of a degree.

Answer

Recall that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side of the triangle. You can solve for the angle by using an inverse tangent function:

$\small \Theta = tan^-^1(\frac{45}{27})=59.03624346792652$ or $59.04$^{\circ}$$ .

Compare your answer with the correct one above

Tap the card to reveal the answer