Solving Right Triangles│Please Help!

Question

Find the missing pieces of the triangle. Round to the nearest tenth.

AC = ?

CB = ?

<A = ?

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Answer 1

Hello,

1. We can easily find m<A.

90 + 23 + m<A = 180 => m<A = 67 deg

1. Now, we can find one of the missing angles. Let's find AC (double-check your calculator; you must use Degree rather than Radian).

sin(23) = AC / 34 => AC = 34 * sin(23) = 13.284858 ~~ 13.3

1. Now use Pythagorean Thm to find BC

BC^2 + 13.284858^2 = 34 ^2

BC = root (34^2 - 13.284858^2) = 31.297165 ~~31.3

So, Answers are AC = 13.3, BC = 31.3, m<A = 67 deg

Answer 2

You can find BC by using SOH-CAH-TOA:

sine = opposite / hypotenuse

opposite (AC) = sin(23º) * 34

adjacent (BC) = cos(23º) * 34

since cosine = adjacent / hypotenuse

After you have calculated AC and BC, you can use the Pythagorean theorem to check your values.

You should always check your work! This is the most fundamental law of solving math problems.

You could also use SOH-CAH-TOA to determine the unknown angle, although it is easy to use the fact that the unknown angle is complementary (adds up to 90 degrees) with the given angle (not the right angle): 90 - 23 = 67 degrees.