# Waecmaths

Title waecmaths question
Question 24

If $\sin x=\tfrac{5}{13}$ and ${{0}^{\circ }}\le x\le {{90}^{\circ }}$ find the value of $(\cos x-\tan x)$

Question 25

An object is 6m away from a mast. The angle of depression of the object from the top of the mast is 50o. Find, correct to 2 decimal places the height of the mast.

Question 26

The bear of Y from X is 060o and the bearing of Z from Y =060o. Find the bearing of X from Z

Question 29

A ship sails x km due east to a point E and continues x km due north to F . Find the bearing of F from the starting point.

Question 33

Given that  $\cos x=\tfrac{12}{13}$evaluate $\frac{1-\tan x}{\tan x}$

Question 38

A man’s eye level is 1.7m above the horizontal ground and 13m from a vertical pole. If the pole is 8.3m high, calculate, correct to the nearest degree, the angle of elevation of the top of the pole from his eyes

Question 18

In diagram $\left| QR \right|=10m,\text{ }\left| SR \right|=8m,$$\angle QPS={{30}^{\circ }},\angle QRP={{90}^{\circ }}\text{ and }\left| PS \right|=x$find x

Question 24

If cos(x + 40o) = 0.0872, what is the value of x?

Question 25

A kite on a taut string of length 50m  inclined at an angle of 54o to the horizontal ground. The height of the kite above the ground is

Question 26

The position of three  ships P, Q and R at sea are illustrated in the diagram . The arrow indicated the North direction. The bearing of Q from P is 050o and $\angle PQR={{72}^{\circ }}$ .Calculate the bearing of R from Q

Question 3

Given that $\cos {{x}^{\circ }}=\tfrac{1}{r}$ express tan xo in terms of r

Question 12

Esther was facing S 20oW. She turned 90o in the clockwise direction. What direction is she facing ?

Question 49

A boy looks through a window of a building and sees a man fruits on the ground 50 m away from the foot of the building. If the windows is  9m from the ground. Calculate, correct to the nearest degree, the angle of depression of the mango from windows

Question 25

Given that $\tan x=1$ where ${{0}^{\circ }}\le x\le {{90}^{\circ }}$ evaluate $\frac{1-{{\sin }^{2}}x}{\cos x}$

Question 26

If $\sin 3y=\cos 2y$ and ${{0}^{\circ }}\le y\le {{90}^{\circ }}$, find the value of y

Question 46

In the diagram $\angle WOX={{60}^{\circ }}$, $\angle YOE={{50}^{\circ }}$and $\angle OXY={{30}^{\circ }}$what is the bearing of X from Y

Question 21

Kweku walked 8m up a slope and was 3m above the ground. If he walks 12m further up the slope, how far above the ground will he be?

Question 26

In the diagram TX is perpendicular to UW, $\left| UX \right|=1cm$and $\left| TX \right|=\left| WX \right|=\sqrt{3}cm$ Find $\angle UTW$

Question 27

If $\cos \theta =x$and $\sin {{60}^{\circ }}=x+0.5$ ${{0}^{\circ }}<\theta <{{90}^{\circ }}$find correct to the nearest degree, the value of θ

Question 49

An object is 6m from the base of a mast. If the angle of depression of the object from the top of the mast is 50o, find, correct to 2 decimal places, the height of the mast

Question 25

Given that $\sin {{60}^{\circ }}=\tfrac{\sqrt{3}}{2}\text{ and }\cos {{60}^{\circ }}=\tfrac{1}{2}$ evaluate $\frac{1-\sin {{60}^{\circ }}}{1+\cos {{60}^{\circ }}}$

Question 26

Find the bearing of X from Y

Question 27

If $\left| XY \right|=50m$ how far east of X is Y?

Question 16

In the diagram $\angle QPR={{90}^{\circ }}$ , if ${{q}^{2}}=25-{{r}^{2}}$ find the value of p

Question 26

If ${{x}^{o}}$ is obtuse, which of the following is true?

Question 27

if $\tan x=1$evaluate $\sin x+\cos x$ leaving your answer in surd form

Question 28

If $\cos {{(x+25)}^{o}}=\sin {{45}^{o}}$, find the value of x

Question 17

In the diagram $\left| LN \right|=4cm,\angle LNM={{90}^{\circ }}$ and $\tan y=\tfrac{2}{3}$What is the area of $\triangle LMN$

Question 30

Q is 32km away from P on a bearing of 042o and R is 25km from P on a bearing of 132o. Calculate the bearing of R from Q

Question 31

In the diagram$\left| PQ \right|=4cm$, $\left| QR \right|=6cm,\text{ }\left| RS \right|=12cm$ $\angle QRS={{90}^{\circ }}$. Find the value of x

Question 33

The bearing of a point P from another point Q is 310o. If $\left| PQ \right|=200M$ how far east of Q is P?

Question 40

$\triangle PQR$ is a equilateral triangle with sides $2\sqrt{3}cm$ calculate its height

Question 10

If tan y = 0.404, where y is acute, find cos 2y

Question 13

In the diagram $\left| QR \right|=5cm$ $\angle PQR={{60}^{\circ }}$ and $\angle PSR={{45}^{\circ }}$. Find $\left| PS \right|$ leaving your answer in surd form

Question 27

In the diagram, P, Q and R  are three points in a plane such that the bearing of R from Q is 110o and the bearing of Q from P is 050o. Find $\angle PQR$

Question 50

A ladder 16m leans against an electric pole. If the ladder makes an angle of 65o with the ground. How far up the electric pole does its top reach

Question 23

Given that  $\tan x=\tfrac{2}{3}$, where ${{0}^{\circ }}\le x\le {{90}^{\circ }}$, find the value of $2\sin x$

Question 24

PQRS is a square. If X is the midpoint of PQ, Calculate correct to the nearest degree, $\angle PXS$

Question 25

The angle of elevation of an aircraft from a point K on the horizontal ground is 30o. If the aircraft is 800m above the ground. How far is it from K?

Question 7

From a point P,R is 5km due west and 12km due south. Find the distance between P and R