Laws of sine and cosine Quiz 1

Question 1

A triangle has $$2$$ angles both of which are $${{30}^{\circ }}$$ degrees with an included side of $$15$$ centimeters. Calculate the area of the triangle. <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/4427c95a-0d86-4a3e-a3ea-aa0274ffe309362171865655617683.png"/>

Accepted Answer

$$A=\dfrac{75\sqrt{3}}{4}$$

Answer

$$A=\dfrac{25\sqrt{3}}{4}$$

Answer

$$A=\dfrac{25\sqrt{3}}{2}$$

Answer

$$A=\dfrac{15\sqrt{3}}{4}$$

Question 2

A right triangle ABC has side lengths $$AC=40$$ meters and $$BC=20\sqrt{3}$$ meters. Calculate the length of $$AB$$.

Accepted Answer

$$20$$

Answer

$$40$$

Answer

$$15\sqrt{3}$$

Answer

$$60$$

Question 3

A triangle $$XYZ$$ has lengths $$XY=10$$, and $$YZ=10\sqrt{2}$$ kilometers. Calculate the side $$XZ$$ given that $$\angle XYZ=105$$ and $$\angle YXZ=45$$.

Accepted Answer

$$AB=-\dfrac{\sqrt{2}-\sqrt{6}}{2}$$

Answer

$$AB=-\dfrac{\sqrt{2}-\sqrt{3}}{2}$$

Answer

$$AB=-\dfrac{\sqrt{2}+\sqrt{6}}{2}$$

Answer

$$AB=\dfrac{\sqrt{2}+\sqrt{3}}{2}$$

Question 4

A triangle with an angle $$30$$ degrees has an adjacent side of length $$10$$ meters which is also the longest side and an angle of $$45$$ degrees that is opposite to the given length. Calculate the area of the triangle.

Accepted Answer

$$A=\dfrac{25\left( 1+\sqrt{3} \right)}{2}$$

Answer

$$A=\dfrac{75\left( 1+\sqrt{3} \right)}{2}$$

Answer

$$A=\dfrac{55\left( 1+\sqrt{3} \right)}{2}$$

Answer

$$A=\dfrac{37.5\left( 2+\sqrt{3} \right)}{2}$$

Question 5

An obtuse triangle ABC had $$2$$ angles $$\angle CAB=45$$ and $$\angle ABC=120$$ with $$AC=20$$ meters. Calculate the length of $$AB$$.

Accepted Answer

$$AB=\dfrac{20\sqrt{3}\sqrt{2-\sqrt{3}}}{3}$$

Answer

$$AB=\dfrac{10\sqrt{3}\sqrt{2-\sqrt{6}}}{3}$$

Answer

$$AB=\dfrac{20\sqrt{3}\sqrt{2-\sqrt{6}}}{3}$$

Answer

$$AB=\dfrac{10\sqrt{3}\sqrt{2-\sqrt{3}}}{3}$$