167,369 views
17 votes
17 votes
Find the number that belongs

in the green box.
4
? 1°
29°
10
Round your answer to the nearest tenth.

Find the number that belongs in the green box. 4 ? 1° 29° 10 Round your answer to-example-1
User Vivek Sable
by
2.7k points

1 Answer

15 votes
15 votes

Answer:

16.6°

Explanation:

The triangle can be solved using the Law of Cosines to find the side opposite the given angle, then the Law of Sines to find the missing angle from the given sides.

__

We choose to use a=10, b=4, C=29°.

c² = a² +b² -2ab·cos(C) . . . . . law of cosines

c² = 10² +4² -2·10·4·cos(29°) ≈ 46.0304

c ≈ √46.0304 ≈ 6.78457

Then angle B (opposite side b) is ...

sin(B)/b = sin(C)/c . . . . . . . . . law of sines

sin(B)/4 = sin(29°)/6.78457

B = arcsin(4/6.78457×sin(29°)) ≈ 16.6085°

The missing acute angle is about 16.6°.

Find the number that belongs in the green box. 4 ? 1° 29° 10 Round your answer to-example-1
User Sanket Singh
by
3.3k points