Question

find the area of the given triangle a = 19, c= 14, B=60°. Round your answer to the nearest tenth. ​

Answer 1

Answer:   115.2 units²

Step-by-step explanation:

Since you know the length of two sides and the measure of the included angle, you can use the following trig formula:

$Area=\dfrac{1}{2}ac \sin B$

Given: a = 19, c = 14, B = 60°

$A=\dfrac{1}{2}(19)(14) \sin 60^o\\\\.\quad =133\sin 60^o\\\\.\quad =115.2$

Answer 2

Answer:

$\huge \boxed{\mathrm{115.2 \ units^2 }}$

Step-by-step explanation:

We can solve for the area of the triangle when two sides are given and the angle in between the two sides.

$\displaystyle A=\mathrm{\frac{1}{2}ac \cdot sinB }$

$\displaystyle A=\mathrm{\frac{1}{2} \cdot 19 \cdot 14 \cdot sin60 }$

$\displaystyle A=\mathrm{\frac{133\sqrt{3} }{2} }$

$\displaystyle A=\mathrm{115.18137870...}$

The area of the triangle is 115.2 units².