Question

Q5 Q30.) Find the measure of the side of the right triangle whose length is designated by a lowercase letter b. Round answers to the nearest whole number.

Answer 1

This answer can be found using cosine.  Cosine is the length of the adjacent side divided by the length of the hypotenuse from the viewpoint of theta.  In this problem, the 37° angle is theta, the hypotenuse is 238 in, and the adjacent side will be represented by x.  The equation would be set up as follows: cos(37)=x/238.  To find x, use basic algebra to multiply each side by 238 to get x=238cos(37).  Next, plug this into a calculator to get ≈182.  Side b is 182 inches.

Answer 2

The length of the side of the right triangle is represented by $\rm{b}$, $190.1\;\rm{inches$.

Given:  a triangle $ABC$, right angled at $C$.

From the figure,

Length of $AB\;\rm{is}\;238\;inches$.

And side $AC\;\rm{is\;reprsented\;by}\;b$.

In $\Delta\;ABC,\;\angle C=90^\circ$

Using trigonometric ratio identities:

$\rm{cos}\;\angle A=\frac{AC}{AB}\\\rm{cos}\;37^\circ=\frac{b}{238}$

$\rm{b}=238\times \rm{cos\;37^\circ}\\\rm{b}=238\times0.79863551\\\rm{b}=190.075251\;\rm{inches\\\\\rm{b} \approx 190.1\;\rm{inches$

Therefore, the length of the side, is represented by $\rm{b}$, is $190.1\;\rm{inches$.

Learn more about Trigonometric ratios here:

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