91Ó°ÊÓ

Explain why an angle of depression is always congruent to an angle of elevation.

Write in simplest radical form the coordinates of each point \(A\) if \(A\) is on the terminal side of an angle in standard position whose degree measure is \(\theta .\) \(O A=4, \theta=45^{\circ}\)

In \(7-12,\) find the cosine of each angle of the given triangle. In \(\triangle A B C, a=4, b=6, c=8\)

Write in simplest radical form the coordinates of each point \(A\) if \(A\) is on the terminal side of an angle in standard position whose degree measure is \(\theta .\) \(O A=15, \theta=135^{\circ}\)

In \(3-14 :\) a. Determine the number of possible triangles for each set of given measures. b. Find the measures of the three angles of each possible triangle. Express approximate values to the nearest degree $$ a=9, c=10, \mathrm{m} \angle C=150 $$

Write in simplest radical form the coordinates of each point \(A\) if \(A\) is on the terminal side of an angle in standard position whose degree measure is \(\theta .\) \(O A=25, \theta=210^{\circ}\)

The length of one of the equal sides of an isosceles triangle measures 25.8 inches and each base angle measures 53 degrees. a. Find the measure of the base of the triangle to the nearest tenth. b. Find the perimeter of the triangle to the nearest inch.

Emily wants to draw a parallelogram with the measure of one side 12 centimeters, the measure of one diagonal 10 centimeters and the measure of one angle 120 degrees. Is this possible? Explain why or why not.

The roof of a shed consists of four congruent isosceles triangles. The length of each equal side of one triangular section is 22.0 feet and the measure of the vertex angle of each triangle is \(75^{\circ} .\) Find, to the nearest square foot, the area of one triangular section of the roof.

A kite is in the shape of a quadrilateral with two pair of congruent adjacent sides. The lengths of two sides are 20.0 inches and the lengths of the other two sides are 35.0 inches. The two shorter sides meet at an angle of \(115^{\circ} .\) a. Find the length of the diagonal between the points at which the unequal sides meet. Write the length to the nearest tenth of an inch. b. Using the answer to part a, find, to the nearest degree, the measure of the angle at which the two longer sides meet.