What is the area of a right triangle when the hypotenuse is 5 cm long and one angle is x/10 radians?

Question

What is the area of a right triangle when the hypotenuse is 5 cm long and one angle is  radians?

Grade 12 Advanced Functions (MHF4U)

Please write neatly and clearly. Thanks

Answer 1

pi/10 radians

= pi/10 times 180/pi = 18 degrees

hypotenuse = 5 cm

opposite angle = 90 degrees

use law of sines

Sin18 /b = Sin90/5

b= base = 5Sin18/Sin90 = 5Sin18/1 = 5Sin18 = about 1.545

altitude = h = square root of (25 -b^2)= about 4.755

Area = hb/2 = about (4.755)(1.545)/2 = about 3.673 square centimeters

You could have worked this problem using radians instead of degrees, but most people are more familiar with using degrees.

Angle C = pi/2 when c= hypotenuse = 5

Angle B = pi/10

then

Angle A = pi- pi/2 -pi/10 = 4p/10 =2p/5

Use law of sines, use a calculator with trig functions and make sure it's in the radian mode