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.

The figure referenced is below:

By the Law of Cosines, the relationship of the measure of an angleof 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.

The figure referenced is below:

By the Law of Cosines, given the lengthsandof two sides of a triangle, and the measureof their included angle, the lengthof the third side can be calculated using the formula

Substituting,,, and, then evaluating:

Taking the square root of both sides:

.

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

用正弦定理公式和solving for:

电动汽车aluating the sines, then calculating:

Based on the information given, we know that the ratio oftoon 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

Based on the information given, we know that the ratio oftoon 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.

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.

First we must solve for when sin is equal to 1/2. That is at

Now, plug it in:

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.