Question

Solve for angles x and y in the triangle below. Round your angle to the nearest whole degree.

x =

y =

42 45 34 48 29 56

Answer 1

Hello !

1. Explanation

A rectangle triangle ABC :

A

I\
I \
I \
I \

B C

1.1 The ratio

We first look for the ratio of the angle.

1.1.1 If the ratio = opposite ; hypotenuse

⇒ It's the sinus.

In the triangle ABC it's :

sin(A) = opposite/hypotenuse

1.1.2 If the ratio = adjacent ; hypotenuse

⇒ It's the cosinus.

In the triangle ABC it's :

cos(A) = adjacent/hypotenuse

1.1.3 If the ratio = opposite ; adjacent

⇒ It's the tangente.

tan(A) = opposite/adjacent

2. Solve x

x has the ratio opposite ; adjacent

⇒ It's the tangente.

tan(x) = opposite/adjacent = 4/6

arctan(4/6) ≈ 33,69 ≈ 34°

3. Solve y

y has the ratio opposite ; adjacent

⇒ It's the tangente.

tan(y) = opposite/adjacent = 6/4

arctan(6/4) ≈ 56,30 ≈ 56°

4. Conclusion

The angle x = 34°

The angle y = 56°

Have a good day!