Question

How do you answer this?

Answer 1

Answer:

  75.7°

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relations between trig functions and sides of a right triangle. You are given all three sides of the triangle, so you can make use of at least two different trig functions to find the missing angle.

  Cos = Adjacent/Hypotenuse

  Tan = Opposite/Adjacent

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cosine

The hypotenuse is 65, and the side adjacent to the unknown angle is 16. That tells you ...

  cos(?) = 16/65

The inverse function is used to find the angle value:

  ? = arccos(16/65) ≈ 75.7°

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tangent

The side opposite the angle of interest is 63. Then you have ...

  tan(?) = 63/16

The inverse function is used to find the angle value:

  ? = arctan(63/16) ≈ 75.7°

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Additional comments

When using trig functions on a calculator, you need to make sure the angle mode is set to what you want. Here, we want angles in degrees, so we have set that as the angle mode. The [DEG] icon in the lower left corner of the display confirms this.

We can't tell what you're supposed to round the value to. The attachment gives enough digits for you to be able to round to whatever precision you need.