Question

Maths Trigonometry Question
100 points up for grabs!
Will give brainliest to whoever answers

Answer 1

Answer:

14) 21.136505024965 m

15) 43.076759215619 km

Step-by-step explanation:

14)

let h be the height of the lighthouse:

tan(41.3) = 18.7/h

Then

h = 18.7÷tan(41.5)

  = 21.136505024965 m

………………………………………

15)

90-71.4 =18.6

Let s be the distance that the plane flew

towards the south:

tan(90 - 71.4) = s/128

Then

tan(18.6) = s/128

Then

s = tan(18.6)×128

  = 43.076759215619 km

Answer 2

14.)

See the diagram below.

Here use tan rule:

$\sf tan(x) = \dfrac{opposite}{adjacent}$

$\sf tan(41+ \frac{30}{60} ) = \dfrac{18.7}{adjacent}$

$\sf adjacent = \dfrac{18.7}{tan(41.5)}$

$\sf adjacent = 21.14$

The height of the lighthouse is 21.14 m.

15.)

See the diagram below.

Here use tan rule:

$\sf tan(x) = \dfrac{opposite}{hypotenuse}$

$\sf tan(18.6) = \dfrac{opposite}{128}$

$\sf opposite = 128 tan(18.6)$

$\sf opposite = 43.08$

The plane travelled 43.08 km far south.