Triangle Trigonometry Worksheet

Triangle Trigonometry Worksheet
• Page 1
1.
In the figure, if $\angle$R = 90°, $\angle$P = 35°25′, $\angle$QSR = 62°30′ and RS = 18.3, then what is the length of PQ?

 a. 43.1 b. 49.4 c. 25 d. 60.7

Solution:

tan 62°30′ = QR18.3
[tan S = QR / SR.]

QR = 18.3 tan 62°30′

QR = 18.3 × (1.920982127)

QR = 35.15

sin 35°25′ = 35.15PQ
[sin P = QR / PQ.]

PQ = 35.15 sin 35°25'

PQ = 60.7
[Simplify using calculator.]

2.
In the figure, if $\angle$C = 90°, $\angle$A = 34°20′, DC = 8.4 and BC = 20.5, then the measure of $\angle$ABD is:

 a. 55°36′ b. 67°44′ c. 22°16′ d. 33°24′

Solution:

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

tan DBC = 0.409756097

DBC = 22°16′

ABD = 180° Ã¢â‚¬â€œ (34°20′ + 90° + 22°16′)

= 180° - 146°36′ = 33°24′

3.
The measure of one acute angle of a right triangle is 78°. Find the other acute angle in the triangle.
 a. 102° b. 12° c. 78° d. 22°

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 78°, then the measure of the other acute angle is 90° - 78° = 12°.

4.
The measure of one acute angle of a right triangle is 32° 43′. The other acute angle of the triangle is:
 a. 58°17′ b. 57°27′ c. 58°43′ d. 57°17′

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° 43′, then the measure of the other acute angle is: 90° - 32° 43′ = 89° 60′ - 32° 43′ = 57° 17′.

5.
The angle of elevation of the top of a pole measures 48° from a point on the ground 18 ft from the base of it. Fnd the height of the flagpole.
 a. 22 ft b. 12 ft c. 18 ft d. 20 ft

Solution:

Let x be the height of the flagpole.

tan 48° = x18

x = 18 tan 48°

x = 18 × (1.110612515) = 20

So, the height of the flagpole is 20 ft.

6.
A pillar of height 200 ft casts a shadow of 320 ft long. Find the measure of the angle of elevation of the sun.
 a. 51°19′ b. 32° c. 58° d. 38°40′

Solution:

Let AB = 200 ft be the length of the pillar.

Let BC = 320 ft be the length of the shadow.

ACB is the angle of elevation of the sun.

tan C = 200320
[tan C = AB / BC.]

tan C = 0.625

C = 32°

7.
In right triangle PQR, if $\angle$Q = 90°, $\angle$R = 22° and $q$ = 35, then the measure of $r$ to two significant digits is ____.

 a. 15 b. 32 c. 13 d. 35

Solution:

sin 22° = r35
[sin R = rq.]

r = 35 × sin 22° = 35 × (0.374606593)

= 13, to two significant digits

8.
In right triangle ABC, if $\angle$B = 90°, $\angle$C = 70° and $c$ = 18, then the measure of $b$ to two significant digits is:

 a. 18 b. 16 c. 19 d. 29

Solution:

sin 70° = 18b
[sin C = cb.]

b = 18sin 70°

b = 18 csc 70°

= 18 (1.064177772) = 19, to two significant digits

9.
In right triangle DEF, if $\angle$D = 42°, $\angle$E = 90° and $f$ = 32, then the measure of $e$ to two significant digits is:

 a. 24 b. 29 c. 43 d. 21

Solution:

cos 42° = 32e
[cos D = fe.]

e = 32cos 42°

e = 32 sec 42°

= 32 × 1.34563273 = 43, to two significant digits

10.
In right triangle PQR if $\angle$Q = 90°, $\angle$R = 30° and $r$ = 12, then the measure of $p$ to two significant digits is:

 a. 21 b. 11 c. 12 d. 24

Solution:

cot 30° = p12
[cot R = pr.]

p = 12 cot 30°

p = 12 × 1.732050808 = 21, to two significant digits.