Question

please help me understand this

12) a) Look at the figure at the right To the nearest degree, what is mLc? 12 0 . Look at the figure on the left. If AC=36, what is the 15 13. length of AB? A B

Answer 1

12 B 8


To find angle C
Given,
Base = 8
Perpedicular = 12
We know that,
$\\\tan C =\mathrm{ \frac{Perpendicular}{Base} } = \frac{12}{8} = \frac{3}{2}\\\\ C = \tan^{-1} \frac{3}{2} = 56.30\degree$




2.

IS 113 B


Let,
AB = x
then, BC = AC - AB = 36 - x
In triangle,
ADB:
$\sin \theta = \frac{AB}{AD} =\frac{x}{15} \;\;\;\;\;\;....(i)$

CDB:
$\sin \theta = \frac{CD}{BC} = \frac{36-x}{13}\;\;\;\;\;\; ....(ii)$
From (i) and (ii):
$\\\frac{x}{15} = \frac{36-x}{13}\\\\ 13x = 36*15-15x\\ 28x = 36*15$
$\\\frac{x}{15} = \frac{36-x}{13}\\\\ 13x = 36*15-15x\\\\ x = \frac{36*15}{28} =19.285$
AB = 19.285