2. Trigonometric Functions on Right Triangles

Given two similar right triangles, one with sides $3$, $4$, and $5$, and the other with sides $6$, $x$, and $10$, what is the value of $x$?

Which of the following is always true about the angles of an isosceles triangle?

Given a right triangle with one acute angle measuring $60°$, how many distinct triangles (up to similarity) can be formed?

In right triangle $PQR$, if $P$ is the right angle, $Q$ = $35°$, and $p$ (opposite $P$) = $8$, what is the measure of angle $R$? Round to the nearest degree.

In a right triangle, if one leg has length $a$ = $6$, the other leg has length $b$ = $8$, and the hypotenuse is $x$, what is the value of $x$?

Given a right triangle QSU with side lengths $\mathrm{QS}=5$ units, $\mathrm{SU}=12$ units, and $\mathrm{UQ}$ as the hypotenuse, what is the perimeter of triangle QSU?

Given an equilateral triangle with height $15$ units, what is the length of side $x$?

In a right triangle, one leg measures $6$ units and the other leg measures $8$ units. Find the length of the hypotenuse. If necessary, round to the nearest tenth.

In triangle $RST$, which is a right triangle with right angle at $S$, if $R$ is $30°$ and the length of side $RS$ is $10$, what is the length of side $ST$?

A right triangle has one leg of length $6$ units and a hypotenuse of length $10$ units. What is the length of the missing leg? If necessary, round your answer to the nearest tenth.

Given an isosceles triangle $ABC$ with angle $B$ equal to $130°$, what is the measure of each of the other two angles?

A right triangle kite has a right angle at vertex N, with side KN adjacent to angle K and side NM adjacent to angle M. If angle K is $30°$ and the hypotenuse KM is $10$ units, what are the lengths of sides KN and NM? KN = $?$ units, NM = $?$ units

A right triangle has a hypotenuse of $14$ units and one leg of $7$ units. What is the length of the other leg?

In the right triangle shown, one leg measures $21$ units and the other leg measures $28$ units. What is the length of the hypotenuse $x$?

Given right triangle QRS with right angle at S, if $\mathrm{QR}$ is the hypotenuse and $\mathrm{QS}$ is $8$ units long, and angle Q is $30°$, what is the length of $\mathrm{RS}$?