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Chapter 8: Q. 46 (page 516)

A right triangle has a hypotenuse of length 10 centimeters. If one angle is 40°, find the length of each leg.

Short Answer

Expert verified

So, the length of each leg is6.42cm,7.66cm,10cm.

Step by step solution

01

Given Information

Given that a right triangle has a hypotenuse of length 10 centimeters and one angle is 40°.

02

Solution

We can draw a figure of the given problem as: -

So in △ABC,∠B=90°

then,

sin(40°)=ABACsin(40°)×AC=ABAB≈0.642×10AB≈6.42cm

Now,

cos(40°)=BCACcos(40°)×AC=BCBC≈0.766×10BC≈7.66cm.

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