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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掳, 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掳.

02

Solution

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

So in 鈻�ABC,鈭�B=90掳

then,

sin(40掳)=ABACsin(40掳)脳AC=ABAB鈮�0.642脳10AB鈮�6.42cm

Now,

cos(40掳)=BCACcos(40掳)脳AC=BCBC鈮�0.766脳10BC鈮�7.66cm.

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