Question

In a certain right triangle, one angle measures pi/11, and the side adjacent to that angle has a length of 13. Find the exact measure of the other non-right triangle and the lengths of the other two sides.

Answer 1

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Answer:

• angle: 9π/22
• opposite side: 13tan(π/11) ≈ 3.817
• hypotenuse: 13sec(π/11) ≈ 13.549

Explanation:

The other acute angle in the triangle is the complement of the given one.

π/2 -π/11 = (11 -2)π/11 = 9π/11 . . . . other acute angle

The trig relation applicable to finding the length of the opposite side is ...

Tan = Opposite/Adjacent

tan(π/11) = Opposite/13

Opposite = 13·tan(π/11) ≈ 3.817

The trig relation relevant to finding the length of the hypotenuse is ...

Cos = Adjacent/Hypotenuse

cos(π/11) = 13/Hypotenuse

Hypotenuse = 13/cos(π/11) = 13sec(π/11) ≈ 13.549