High School

I have a right triangle with the hypotenuse labeled as \( c \) and the side opposite the 62-degree angle labeled as \( b \). The triangle does not have a label for the adjacent side. The bottom left corner of the triangle is 62 degrees, and the bottom right corner is 90 degrees. Round your answer to the nearest 16th of an inch.

Answer :

Question is incomplete. Answering in a general way;

The side CA has a length of [tex]\sqrt{c^{2}-b^{2} }[/tex] and Angle C is of 28 degrees.

Given,

Right angled triangle ABC

Length of side AB = b

Length of side BC = c

Angle B = 62°

Angle A = 90°

We have to find the length of side CA and Angle C;

Here,

According to Pythagorean theorem,

Hypotenuse = [tex]\sqrt{base^{2}+altitude^{2} }[/tex]

Here,

Altitude = [tex]\sqrt{Hypotenuse^{2} -Base^{2} }[/tex]

CA = [tex]\sqrt{c^{2} -b^{2} }[/tex]

Now,

Sum of interior angles of a triangle is 180°

Then,

∠A + ∠B + ∠C = 180°

So,

90° + 62° + ∠C = 180°

∠C = 180° - 152°

∠C = 28°

That is,

The length of side CA is [tex]\sqrt{c^{2}-b^{2} }[/tex] and Angle C is 28°

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