2. Trigonometric Functions on Right Triangles

Given a right triangle with angle $A$, which of the following expressions can be used to find the measure of angle $A$? Select three options.

In a right triangle, if one of the acute angles measures $62°$, what is the measure of the other acute angle?

A right triangle is shown below. Which ratio gives the cosine of $\angle B$?

In Exercises 9–16, use the given triangles to evaluate each expression. If necessary, express the value without a square root in the denominator by rationalizing the denominator.

sin 𝜋/4 - cos 𝜋/4

Which trigonometric function is typically used to find the angle of elevation from a point on the ground to the top of a building when the height of the building $h$ and the horizontal distance from the building $d$ are known?

Given a right triangle with angle $A$ and sides $a$ (opposite), $b$ (adjacent), and $c$ (hypotenuse), which of the following expressions can be used to find the measure of angle $A$? Select one correct option.

Given that $\cos \left(\theta \right)$ = $\frac{3}{10}$, what is the value of $\sin \left(\theta \right)$ if $\theta$ is an acute angle?

Given two right triangles, $△\mathrm{PQR}$ with sides PQ = $3$, QR = $4$, and RP = $5$, and $△\mathrm{STU}$ with sides ST = $5$, TU = $12$, and US = $13$, which angle has a sine ratio of $\frac{3}{5}$?

Solve each problem. (Source for Exercises 49 and 50: Parker, M., Editor, She Does Math, Mathematical Association of America.) Length of Sides of an Isosceles Triangle An isosceles triangle has a base of length 49.28 m. The angle opposite the base is 58.746°. Find the length of each of the two equal sides.

If you are given two $\mathrm{angles}$ in a $\mathrm{right}\mathrm{triangle}$, what additional information do you need to determine all the $\mathrm{side}\mathrm{lengths}$ of the $\mathrm{triangle}$?

Given a right triangle with sides $a$, $b$, and hypotenuse $c$, and angle $\theta$ opposite side $a$, which of the following correctly expresses $\sin \theta$ in terms of the triangle's sides?

In a right triangle, if angle $cbe$ is one of the non-right angles and the other non-right angle measures $72°$, what is the measure of angle $cbe$?

In right triangle $ABC$, angle $BAC$ measures $56°$. What is the measure of angle $BDC$ if $D$ is a point on $AC$ such that $BD$ is perpendicular to $AC$?

Omar wants to determine $cos\theta$ in a right triangle. If the length of the adjacent side to angle $\theta$ is 5 units and the hypotenuse is 13 units, what is $cos\theta$?

In a right triangle, which pair of angles are $\mathrm{linear}\mathrm{pairs}$?