Question

Need help with 5 and 6 Institutions: Find the measure of each angle Calculate the length of each side

Answer 1

#5

ABC is a right triangle with

The leg AC = 7.6

The hypotenuse AB = 12

To solve the triangle we have to find

BC

To find BC we will use the Pythagoras relation

$(leg_1)^2+(leg_2)^2=(hypotenuse)^2$

Let leg1 = AC and leg2 = BC

The hypotenuse = AB

Then the rule will be

$(AC)^2+(BC)^2=(AB)^2$

Substitute AC by 7.6 and AB by 12

$\begin{gathered} 7.6^2+BC^2=12^2 \\ 57.76+BC^2=144 \end{gathered}$

Subtract both sides by 57.76 and find the square root of each side

$\begin{gathered} 57.76-57.76+BC^2=144-57.76 \\ BC^2=86.24 \\ \sqrt{BC^2}=\sqrt{86.24} \\ BC=9.286549413 \end{gathered}$

Round it to the nearest tenth

BC = 9.3

To find $cosA=\frac{adjacent}{hypotenuse}$The adjacent side of The hypotenuse is AB

$\begin{gathered} cosA=\frac{AC}{AB} \\ \\ cosA=\frac{7.6}{12} \end{gathered}$

To find angle A we will use the inverse of cosine

$\begin{gathered} A=cos^{-1}(\frac{7.6}{12}) \\ A=50.70351976^{\circ} \end{gathered}$

Round it to the nearest tenth

A = 50.7 degrees

Since the sum of angles of a triangle is 180 degrees

Then to find $\begin{gathered} B=180-90-50.7 \\ B=39.3^{\circ} \end{gathered}$

B = 39.3 degrees