# Solving Right Triangles Worksheet

Solving Right Triangles Worksheet
• Page 1
1.
In the figure if $\angle$R = 90°, $\angle$P = 35° 25′, $\angle$QSR = 62° 30′ and RS = 20.3, then what is the length of PQ?

 a. 47.86 b. 67.3 c. 22.6 d. 31.78

#### Solution:

In right triangle SRQ, tan 62° 30′ = QR20.3
[Use tan S = QR / SR.]

QR = 20.3 tan 62° 30′

QR = 20.3 × (1.920982127)
[Use calculator for tan 62° 30′.]

QR = 39
[Simplify.]

In right triangle PRQ, sin 35° 25′ = 39PQ
[Use sin P = QR / PQ.]

PQ = 39sin35o25'
[Simplify.]

PQ = 67.3

2.
In the figure if $\angle$C = 90°, $\angle$A = 34°20′, DC = 8.4 and BC = 20.5, then find the measure of $\angle$ABD.
 a. 55°36′ b. 22°16′ c. 33°24′ d. 67°44′

#### Solution:

tan DBC = 8.420.5
[tan DBC = DC / BC.]

tan DBC = 0.409756097

DBC = 22°16′

ABD = 180° - (34°20′ + 90° + 22°16′)

= 180° - 146°36′ = 33°24′

3.
The measure of one acute angle of a right triangle is 65°. Find the measure of the other acute angle of the triangle.
 a. 115° b. 90° c. 25° d. 75°

#### Solution:

The sum of the measures of the two acute angles of a right triangle is 90°.

If one acute angle of a right triangle is 65°, then the measure of the other acute angle is: 90° - 65° = 25°

4.
The measure of one acute angle of a right triangle is 32° 46′. Then find the measure of the other acute angle of the triangle.
 a. 57°60′ b. 122°46′ c. 62°14′ d. 57°14′

#### Solution:

The sum of the measures of the two acute angles of a right triangle is 90°.

If one acute angle of a right triangle is 32° 46′, then the measure of the other acute angle is: 90° - 32° 46′ = 89° 60′ - 32° 46′ = 57° 14′.

5.
The angle of elevation of the top of a pole measures 48° from a point on the ground 18 ft away from its base. Find the height of the flagpole approximately.
 a. 16 ft b. 12 ft c. 20 ft d. 27 ft

#### Solution:

Let x be the height of the flagpole and y be the distance of the point from its base.

In right triangle, tan 48° = x18
[Use tan 48° = xy.]

x = 18 tan 48°
[Cross multiply.]

x = 18 × (1.110612515) 20
[Use calculator for tan 48°.]

So, the height of the flagpole is 20 ft.

6.
A pillar of height 244 ft casts a shadow of 363 ft long. Find the measure of the angle of elevation of the sun.
 a. 56° b. 48° c. 42° d. 34°

#### Solution:

Length of the pillar, a = 244 ft.

Length of the shadow, b = 363 ft.

ACB is the angle of elevation of the sun.

In right triangle ABC, tan C = 244363
[Use tan C = AB / BC = ab.]

tan C = 0.672176
[Simplify.]

C = 34°
[Use calculator to find the measure of C.]

So, angle of elevation of the sun is 34°

7.
In right triangle PQR, if $\angle$Q = 90°, $\angle$R = 22° and $q$ = 45, then find the measure of $r$ to two significant digits.

 a. 17 b. 38 c. 67 d. 45

#### Solution:

In right triangle PQR, sin 22° = r45
[Use sin R = rq.]

r = 45 × sin 22° = 45 × (0.374606593)
[Use calculator for sin 22°.]

= 17, to two significant digits.
[Simplify.]

8.
In right triangle ABC, if $\angle$B = 90°, $\angle$C = 75° and $c$ = 18, then estimate the measure of $b$.

 a. 19 b. 4 c. 18 d. cannot be determined

#### Solution:

In right triangle ABC, sin 75° = 18b
[Use sin C = cb.]

b = 18sin75o

b = 18 csc 75°
[Use calculator for csc 75o.]

= 18 (1.03527599) 19
[Simplify.]

9.
In right triangle DEF if $\angle$D = 42°, $\angle$E = 90° and $f$ = 29, then find the measure of $e$ to two significant digits.

 a. 12 b. 19 c. 29 d. 39

#### Solution:

In right triangle DEF, cos 42° = 29e
[Use cos D = fe.]

e = 29cos 42°
[Cross multiply.]

e = 29 sec 42°
[Use sec 42° = 1cos 42°.]

= 29 × 1.34563273 = 39, to two significant digits.
[Use calculator for sec 42°.]

10.
In right triangle PQR if $\angle$Q = 90°, $\angle$R = 30° and $r$ = 22, then find the measure of $p$ to two significant digits.

 a. 13 b. 19 c. 38 d. 11

#### Solution:

In right triangle PQR, cot 30° = p22
[Use cot R = pr.]

p = 22 cot 30°
[Cross multiply.]

p = 22 × 1.732050808 = 38, to two significant digits.
[Simplify.]