If $\sin \theta =\tfrac{12}{13}$ find the value of $1+\cos \theta $

If $\tan \theta =\tfrac{3}{4}$,  find the value of  $\sin \theta +\cos \theta$

In a triangle PQR, q =8cm,r = 6cm and$\cos P=\tfrac{1}{12}$. Calculate the value of p

A man stands on a tree 150cm high and see a boat at an angle of depression of 74^o, Find the distance of the boat from the base of the tree.

If angle θ is 135^o, evaluate cos θ

A man walks 100m due west from a point X to Y, he then walks 100m due North to a point Z. Find the bearing of X from Z

In a right angle triangle, if tan θ = ¾ what is cos θ – sin θ

If the area of $\vartriangle PQR$above is $12\sqrt{3}$cm², find the value of q?

If $\cot \theta =\tfrac{8}{15},\text{ where }\theta \text{ is acute, find }\sin \theta $

A cliff on the bank of a river is 300 metres high. If the angles of depression of a point on the opposite side of the river is 60^o. Find  the width of the river.