Question

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

A = 12° 54', b = 6.812 cm

B = ______ °_________ '

a = _________cm

c = _________cm

Answer 1

B=77° 44'

a=6.649 cm

c=1.479 cm

Explanation:

Given

A = 12° 54'=12.54°,

C=90°

b = 6.812 cm

Required:

B = ______ °_________ '=?

a = _________cm

c = _________cm

Solution:

B = ______ °_________ '=?

As we know that sum of angles in a triangle is 180

sum A+B+C=180

12.54+B+90=180

B+102.54=180

subtracting 102.54 from both sides, we get

B=77.46°

B = 77 ° 44 '

a = _________cm

As we know that

`cos\theta=base/hypotenous\\\\cos\theta=a/b\\\\\theta=12.54\\\\cos(12.54)=a/6.812\\\\a=cos(12.54)*6.812\\\\a=0.976*6.812\\\\a=6.649cm`

c = _________cm=?

As we know that

`sin\theta=perpendicular/hypotenous\\\\sin\theta=b/c\\\\\theta=12.54\\\\sin(12.54)=6.812/c\\\\c=sin(12.54)*6.812\\\\c=0.217*6.812\\\\c=1.479cm`