A)
[tex]\begin{gathered} c=17.159 \\ A=4.747\text{\operatorname{\degree}} \\ B=85.253\operatorname{\degree} \end{gathered}[/tex]
Explanation
Explanation
Step 1
c) to find the measure of the hypotenuse we can use the Pythagorean theorem, it states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)
[tex]a^2+b^2=c^2[/tex]
Step 1
a) Let
[tex]\begin{gathered} a=1.42 \\ b=17.1 \end{gathered}[/tex]
b) now, replace and solve for c
[tex]\begin{gathered} a^2+b^2=c^2 \\ 1.42^2+17.1^2=c^2 \\ 294.4264=c^2 \\ c=\sqrt{294.4264} \\ c=17.15885 \\ rounded \\ c=17.159 \end{gathered}[/tex]
Step 2
angle A
to solve for angle A we can use tan function, so
[tex]tan\theta=\frac{opposite\text{ side}}{adjacent\text{ side}}[/tex]
replace
[tex]\begin{gathered} tan\text{ A=}\frac{a}{b} \\ tanA=\frac{1.42}{17.1} \\ A=\tan^{-1}(\frac{1.42}{17.1}) \\ A=4.747\text{ \degree} \end{gathered}[/tex]
Step 3
for angle B we can use tan function
let
[tex]\begin{gathered} opposit\text{ side=b} \\ adjacent\text{ side=a} \end{gathered}[/tex]
replace and solve for angle B
[tex]\begin{gathered} tan\text{ B=}\frac{b}{a} \\ tanB=\frac{17.1}{1.42} \\ B=\tan^{-1}(\frac{17.1}{1.42}) \\ B=85.252\text{ \degree} \\ \end{gathered}[/tex]
I hope this helps you
