Question

Help please triangles and trig

Answer 1

Answer:

$\sin L = \frac{3}{5}$

$\tan N = \frac{4}{3}$

$\cos L = \frac{4}{5}$

$\sin N = \frac{4}{5}$

Step-by-step explanation:

Given

The above triangle

First, we calculate the length LM using Pythagoras theorem.

$LN^2 = LM^2 + MN^2$

$10^2 = LM^2 + 6^2$

$100 = LM^2 + 36$

Collect like terms

$LM^2 = 100 - 36$

$LM^2 = 64$

Take positive square root

$LM=8$

Solving (a): Sin L

$\sin L = \frac{Opposite}{Hypotenuse}$

$\sin L = \frac{MN}{LN}$

$\sin L = \frac{6}{10}$

Simplify

$\sin L = \frac{3}{5}$

Solving (b): tan N

$\tan N = \frac{Opposite}{Adjacent}$

$\tan N = \frac{LM}{MN}$

$\tan N = \frac{8}{6}$

Simplify

$\tan N = \frac{4}{3}$

Solving (c): cos L

This calculated as:

$\cos L = \frac{Adjacent}{Hypotenuse}$

$\cos L = \frac{LM}{LN}$

$\cos L = \frac{8}{10}$

Simplify

$\cos L = \frac{4}{5}$

Solving (d): sin N

This is calculated using:

If $a + b = 90$

Then: $\sin a = \cos b$

So:

$\sin N = \cos L$

$\sin N = \frac{4}{5}$