A.) Use a calculator to find a value of between 0° and 90° that satisfies the st

Question

A.) Use a calculator to find a value of between 0° and 90° that satisfies the statement. Write your answer in degrees and minutes rounded to the nearest minute.

csc = 18.8975

B.) This problem refers to right triangle ABC with C = 90°. Solve for all the missing parts using the given information. (Round your answers to one decimal place.)

A = 35.2°, a = 43.5 inches

what is a and b in ft?

C.) This problem refers to right triangle ABC with C = 90°. Solve for all the missing parts using the given information. (Round your answers to one decimal place.)

B = 24°, c = 4.1 ft

what is side a and b in Ft?

D.)This problem refers to right triangle ABC with C = 90°. Solve for all the missing parts using the given information. (Round your answers to one decimal place.)

b = 364.8 inches, c = 597.7 inches

what is angle A and B in degrees?

E.) The circle in the figure below has a radius of r and center at C. The distance from A to B is x. Redraw the figure below, label as indicated in the problem, and then solve the problem.

If C = 61° and x = 23, find r. (Round your answer to the nearest whole number.)

what is R?

Explanation / Answer

cosec theta = 18.8975

sin theta = 1 / 18.8975

theta = sin ^-1 ( 1 / 18.8975 )

3 degrees + .0333 deg

1 deg = 60'

.0333 deg = 60*.0333 = 1.998'

theta = 3 degrees 2minutes

b ) for the right angled triangle

tan 35.2 = perpendicular / base

tan 35.2 = 43.5 / base

.7054 = 43.5 / base

base ( b) = 43.5 / .7054 = 61.66 inches

converting inches to feet

a = 43.5 inches = 3.625 feet

b = 61.66 inches = 5.138 feet

c ) for right angled triangle ABC

sin 24 = perpendicular / hypotenuse

.4067 = b / 4.1

b = 1.667 feet

cos 24 = base / hypotenuse

.9135 = a / 4.1

a = 3.7455 feet

E )

angle C = 61 degrees

taking the right angle triangle CDA

we can write

cos 61 = base / hypotenuse

base = r

hypotenuse = r + x = r + 23

therefore,

cos 61 = r / ( r + 23 )

.4848 = r / ( r + 23 )

multiplying both sides by ( r+ 23 )

.4848r + 11.15 = r

on solving we get

r = 11.15 / .5152

r = 21.64

r = 22 ( round off )

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