2. Trigonometric Functions on Right Triangles

In the context of solving right triangles, what is the first step in the standard construction of the perpendicular bisector of segment $mn$?

A kite-shaped quadrilateral has sides of lengths $5$ cm and $7$ cm, and the shorter diagonal is $8$ cm. What is the length of the kite's longer diagonal?

In right triangle $ABC$, angle $B$ is the right angle, $A$ is at the origin, $B$ is at $(0,4)$, and $C$ is at $(3,0)$. What is the length of line segment $AC$? Round to the nearest tenth.

A right triangle has one angle that measures $80°$. What is the measure of the other acute angle?

Given a right triangle with hypotenuse length $c$ and height $a$, which formula can be used to find the length of the base $b$?

In a right triangle, angle $A$ is $35°$ and the side opposite angle $A$ is $7$ units long. The hypotenuse is $12$ units long. Solve for angle $x$ (the other non-right angle). Round your answer to the nearest tenth of a degree, if necessary.

A right triangle has one leg measuring $18\mathrm{mm}$ and a hypotenuse measuring $24\mathrm{mm}$. What is the length of the missing leg?

In right triangle $RST$, angle $R$ is the right angle, $S$ is at the top, and $T$ is at the bottom right. If $RS$ = $6$ units and $RT$ = $8$ units, what is the length of side $TS$?

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 $x$?