2. Trigonometric Functions on Right Triangles

A right triangle has one angle that measures $20°$. What is the measure of the other acute angle?

Given a right triangle where the length of one leg is $x_s=10$ and the length of the other leg is $x_y=24$, what is the length of the hypotenuse $r_y$?

In a right triangle, one leg measures $6$ units, the other leg measures $8$ units, and the hypotenuse is labeled $x$. What is the value of $x$?

In a right triangle, two interior angles each measure $34°$. Which of the following statements is true about this triangle?

Which statement proves that triangle $xyz$ is an isosceles right triangle?

In a right triangle, one leg measures $8yd$ and the hypotenuse measures $64yd$. What is the length of the other leg?

Given a right triangle where $tv$ = $24$ and $xz$ = $13$, what is the value of $vw-yz$?

Given a right triangle with one leg measuring $5$ units and the hypotenuse measuring $8.6$ units, which of the following is the length of the unknown side rounded to the nearest whole number?

CONCEPT PREVIEW Match each equation in Column I with the appropriate right triangle in Column II. In each case, the goal is to find the value of x.

x = 5 tan 38°

In the right triangle shown, the length of $a$ is $6$ units and the length of $b$ is $8$ units. What is the length of the hypotenuse $c$?

In a right triangle $ABC$ with $A$ as the right angle and the triangle is isosceles, what is the length of each leg if the hypotenuse is $16$ units?

Given a right triangle where one of the acute angles $x$ has a measure of $51°$, how many distinct triangles (up to similarity) can be formed?

Solve each right triangle. In Exercise 46, give angles to the nearest minute. In Exercises 47 and 48, label the triangle ABC as in Exercises 45 and 46. A = 39.72°, b = 38.97 m

Solve each right triangle. In Exercise 46, give angles to the nearest minute. In Exercises 47 and 48, label the triangle ABC as in Exercises 45 and 46.

Solve each right triangle. In each case, C = 90°. If angle information is given in degrees and minutes, give answers in the same way. If angle information is given in decimal degrees, do likewise in answers. When two sides are given, give angles in degrees and minutes. See Examples 1 and 2. a = 958 m, b = 489 m