All SAT II Math I Resources
Example Questions
Example Question #1 : Trigonometry
A plane flies degrees north of east for
miles. It then turns and flies
degrees south of east for
miles. Approximately how many miles is the plane from its starting point? (Ignore the curvature of the Earth.)
The plane flies two sides of a triangle. The angle formed between the two sides is 40 degrees. In a Side-Angle-Side situation, it is appropriate to employ the use of the Law of Cosines.
Example Question #1 : Trigonometry
In :
Evaluate to the nearest degree.
Insufficient information is provided to answer the question.
The figure referenced is below:
By the Law of Cosines, the relationship of the measure of an angle of a triangle and the three side lengths
,
, and
,
the sidelength opposite the aforementioned angle, is as follows:
All three sidelengths are known, so we are solving for . Setting
. the length of the side opposite the unknown angle;
;
;
and ,
We get the equation
Solving for :
Taking the inverse cosine:
,
the correct response.
Example Question #1 : Finding Sides With Trigonometry
In :
Evaluate the length of to the nearest tenth of a unit.
The figure referenced is below:
By the Law of Cosines, given the lengths and
of two sides of a triangle, and the measure
of their included angle, the length
of the third side can be calculated using the formula
Substituting ,
,
, and
, then evaluating:
Taking the square root of both sides:
.
Example Question #1 : Trigonometry
In :
The figure referenced is below:
The Law of Sines states that given two angles of a triangle with measures , and their opposite sides of lengths
, respectively,
,
or, equivalently,
.
In this formula, we set:
, the desired sidelength;
, the measure of its opposite angle;
, the known sidelength;
, the measure of its opposite angle, which is
Substituting in the Law of Sines formula and solving for :
Evaluating the sines, then calculating:
Example Question #1 : Trigonometry
What is the measure of the angle made between a line segment with points ,
and the
-axis? Round your answer to the nearest hundreth of a degree.
No angle measure can be calculated
Based on the information given, we know that the ratio of to
on this segment could be represented as:
This ratio represents the tangent of the triangle formed by our line segment and the -axis. Using the inverse tangent function, we can find the angle measure:
This refers to a reference angle of
Example Question #1 : Trigonometry
What is the measure of the angle made between a line segment with points ,
and the
-axis? Round your answer to the nearest hundreth of a degree.
No angle can be calculated
Based on the information given, we know that the ratio of to
on this segment could be represented as:
This ratio represents the tangent of the triangle formed by our line segment and the -axis. Using the inverse tangent function, we can find the angle measure:
This refers to a reference angle of .
Example Question #1 : Trigonometry
A triangle is formed by connecting the points . Determine the elevation angle to the nearest integer in degrees.
After connecting the points on the graph, the length of the triangular base is 1 unit.
The height of the triangle is 6. To find the elevation angle, the angle is opposite from the height of the triangle. Since we know the base and the height, the elevation angle can be solved by using the property of tangent.
The best answer is .
Example Question #1 : Trigonometry
Solve for between
.
First we must solve for when sin is equal to 1/2. That is at
Now, plug it in:
Example Question #621 : Sat Subject Test In Math I
Solve for between
.
First we must solve for when sin is equal to 1/2. That is at
Now, plug it in:
Example Question #1 : Sine, Cosine, Tangent
In a triangle, , what is the measure of angle A if the side opposite of
angle A is 3 and the adjacent side to angle A is 4?
(Round answer to the nearest tenth of a degree.)
To find the measure of angle of A we will use tangent to solve for A. We know that
In our case opposite = 3 and adjacent = 4, we substitute these values in and get:
Now we take the inverse tangent of each side to find the degree value of A.
All SAT II Math I Resources
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