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In an isosceles triangle, the base is 28 cm long, and the legs are 17 cm long. Now do you find the measure of a base angle to the nearest degree?

Answer 1

First, draw a diagram to represent the situation

Cut the base in half so that there is a perpendicular line making a midpoint on the base at 14 cm.

Use the basic trigonometric ratios to find the angle to the far left of the diagram. Since we know the side adjacent to the angle (14 cm) and the hypotenuse (17 cm), we use cosine to find the missing angle.

Assuming ø represents the angle we are looking to find:

Cos ø = #14/17#

ø = #Cos^-1#(#14/17#)

ø ≈ 35˚

The two base angles measure approximately 35˚ each.

Hopefully you understand now!

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Answer 2

Allison Allen

Using the properties of an isosceles triangle, the measure of a base angle can be found using the inverse cosine function:

Base angle measure ≈ arccos((17^2) / (2 * 17^2)) ≈ 56°.

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