# Find the value of side b, the value of angle A,  and the value of angle B.

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## Expert Answers

The length of side b can be calculated in two ways:

1. Using the Pythagorean theorem

`b=sqrt(25^2-20^2)=15`

2. Noting that this triangle is a multiple of a 3-4-5 right triangle where the legs are 3 and 4 and the hypotenuse is 5. For this right triangle, the legs are 3x5=15...

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The length of side b can be calculated in two ways:

1. Using the Pythagorean theorem

`b=sqrt(25^2-20^2)=15`

2. Noting that this triangle is a multiple of a 3-4-5 right triangle where the legs are 3 and 4 and the hypotenuse is 5. For this right triangle, the legs are 3x5=15 and 4x5=20 and the hypotenuse is 5x5=25.

Angle A can be determined using any of the trigonometric functions. If we apply the sine function to determine the measure of angle A, we get:

`sin A=20/25=0.8`

`A=sin^-1(0.8)=53.13`o

The sum of the two oblique angles of a right triangle is 90 degrees, therefore:

`B=90-53.13=36.87`o

Therefore b=15, A=53.13 degrees and B=36.87 degrees.

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