All HiSET: Math Resources
Example Questions
Example Question #91 : Measurement And Geometry
Evaluate in terms of
.
Suppose we allow be the lengths of the opposite leg and adjacent leg and the hypotenuse, respectively, of the right triangle with an acute angle measuring
.
The tangent of the angle is the ratio of the length of the opposite leg to that of the adjacent leg, so
We can set the lengths of the opposite and adjacent legs to and 5, respectively. The length of the hypotenuse can be determined using the Pythagorean Theorem:
The sine of the angle is equal to the ratio of the length opposite leg to that of the hypotenuse, so
.
Example Question #1 : Problems Involving Right Triangle Trigonometry
Evaluate in terms of
.
Suppose we allow be the lengths of the opposite leg and adjacent leg and the hypotenuse, respectively, of the right triangle with an acute angle measuring
. The cosine is defined to be the ratio of the length of the adjacent side to that of the hypotenuse, so
We can set the lengths of the adjacent leg and the hypotenuse to and 3, respectively. By the Pythagorean Theorem, the length of the opposite leg is
The sine of the angle is equal to the ratio of the length of the opposite leg to that of the hypotenuse, so
.
Example Question #1 : Problems Involving Right Triangle Trigonometry
Evaluate in terms of
.
Suppose we allow be the lengths of the opposite leg and adjacent leg and the hypotenuse, respectively, of the right triangle with an acute angle measuring
.
The tangent of the angle is the ratio of the length of the opposite leg to that of the adjacent leg, so
We can set the lengths of the opposite and adjacent legs to and 5, respectively. The length of the hypotenuse can be determined using the Pythagorean Theorem:
The cosine of the angle is equal to the ratio of the length of the adjacent leg to that of the hypotenuse, so
.
Example Question #101 : Measurement And Geometry
None of the other choices gives the correct response.
None of the other choices gives the correct response.
An identity of trigonometry is
for any value of .
Since , it immediately follows that
.
This response is not among the given choices.
Example Question #1 : Problems Involving Right Triangle Trigonometry
Refer to the triangle in the above diagram. Which of the following expressions correctly gives its area?
None of the other choices gives the correct response.
The area of a right triangle is half the product of the lengths of its legs, which here are and
- that is,
We are given that .
is the leg opposite the angle
and
is its adjacent leg, we can find
using the tangent ratio:
Setting and
, we get
Solve for by multiplying both sides by 12:
Now, set and
in the area formula:
,
the correct choice.
Example Question #1 : Problems Involving Right Triangle Trigonometry
Refer to the triangle in the above diagram. Which of the following expressions correctly gives its area?
None of the other choices gives the correct response.
The area of a right triangle is half the product of the lengths of its legs, which here are and
- that is,
We are given that .
is the leg opposite the angle
and
is its adjacent leg, we can find
using the tangent ratio:
Setting and
, we get
Solve for by first, finding the reciprocal of both sides:
Now, multiply both sides by 8:
Now, set and
in the area formula:
,
the correct choice.
Example Question #1 : Problems Involving Right Triangle Trigonometry
Evaluate in terms of
.
Suppose we allow be the lengths of the opposite leg and adjacent leg and the hypotenuse, respectively, of the right triangle with an acute angle measuring
. The cosine is defined to be the ratio of the length of the adjacent side to that of the hypotenuse, so
We can set the lengths of the adjacent leg and the hypotenuse to and 3, respectively. By the Pythagorean Theorem, the length of the opposite leg is
The tangent of the angle is the ratio of the length of the opposite leg to that of the adjacent leg, so
.
Example Question #1 : Problems Involving Right Triangle Trigonometry
The sine of an angle is defined to be the ratio of the length of the opposite leg of a right triangle to the length of its hypotenuse. Therefore, we can set . By the Pythagorean Theorem:
the adjacent leg of the triangle has measure
The tangent of the angle is the ratio of the length of the opposite leg to that of the adjacent leg, which is
,
the correct response.
All HiSET: Math Resources
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