Question

1. Find the missing side length. Round your answer to the nearest tenth.

Answer 1

QUESTION 1

We can use the cosine rule to find the missing side length.

Recall that the cosine rule for a triangle with sides a,b,c and an included angle A is

$a^2=b^2+c^2-2bc\cos A$

Let the missing side length in the triangle with sides 6, 9 and the included angle of $37\degree$ be $a$ units.

We then substitute the values into the cosine rule to obtain;

$a^2=6^2+9^2-2(6)(9)\cos 37\degree$

$a^2=36+81-108\cos 37\degree$

$a^2=30.747$

$\Rightarrow a=\sqrt{30.747}$

$\Rightarrow a=\sqrt{30.747}$

$\Rightarrow a=5.5$ units to the nearest tenth.

QUESTION 2

We again use the cosine rule: $a^2=b^2+c^2-2bc\cos A$

We substitute the given values to obtain;

$a^2=11^2+13^2-2(11)(13)\cos 108\degree$

$a^2=121+169-286\cos 108\degree$

$a^2=378.379$

$\Rightarrow a=\sqrt{378.379}$

$\Rightarrow a=19.5$ to the nearest tenth

QUESTION 3

We again use the cosine rule :

$|BA|^2=(\frac{1}{2})^2+(\frac{1}{3})^2-2(\frac{1}{2})(\frac{1}{3})\cos 100\degree$

$|BA|^2=0.418899$

$|BA|=\sqrt{0.418899}$

$|BA|=0.65$ to the nearest hundredth