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Solving Right Triangles Worksheet

Solving Right Triangles Worksheet
  • Page 1
 1.  
In the figure if R = 90°, P = 35° 25′, 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


Correct answer : (2)
 2.  
In the figure if C = 90°, A = 34°20′, DC = 8.4 and BC = 20.5, then find the measure of 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′


Correct answer : (3)
 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°


Correct answer : (3)
 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′.


Correct answer : (4)
 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.


Correct answer : (3)
 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°


Correct answer : (4)
 7.  
In right triangle PQR, if Q = 90°, 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.]


Correct answer : (1)
 8.  
In right triangle ABC, if B = 90°, 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.]


Correct answer : (1)
 9.  
In right triangle DEF if D = 42°, 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°.]


Correct answer : (4)
 10.  
In right triangle PQR if Q = 90°, 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.]


Correct answer : (3)

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