Question

a. Write tan 30 and tan 60 in terms of the given measurements.


b. Prove that h = √ab c. If a= 12, B = 3, then what is the area of the triangle ABC.​

Answer 1

Answer:

Step by Step Explanation:

a.

$tan B = \frac{h}{a} \\\frac{1}{\sqrt{3} } = \frac{h}{a} .... 1\\\\tan C =\frac{h}{b} \\\\\frac{\sqrt{3} }{1} = \frac{h}{b} .... 2$

Multiplying equations 1 and 2

$\frac{h}{a} * \frac{h}{b} = 1\\h^{2} = ab\\h=\sqrt{ab}$

b.

h=$\sqrt{36}$

h=6

a+b=15

Area of the triangle=

$\frac{1}{2} * base * height\\= \frac{1}{2} * 15* 6\\= 45 sq. units$