Question

In triangle PQR , right angled at Q, PQ=3cm and PR=6cm . Determine angle P and angleR

Answer 1

Answer:

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Answer 2

Answer :

The measurements are :

angle P is 60°

angle R is 30°

Given :

• PQR is a right angled triangle , right angled at Q
• sides PQ = 3cm and PR = 6cm

To Determine :

The measurements of angle P and angle R

Concept to be used :

The trigonometric functions :

• $\sf \sin \theta = \dfrac{perpendicular}{hypotenus}$

• $\sf \cos \theta = \dfrac{base}{hypotenus}$

• $\sf \tan \theta = \dfrac{perpendicular}{base}$

Solution :

Using the trigonometric function cos to determine angle P

$\sf \cos P = \dfrac{PQ}{PR} \\\\ \implies \sf \cos P = \frac{3cm}{6cm} \\ \\ \implies \sf \cos P = \frac{1}{2} \\ \\ \sf \implies \cos P = \cos60 \degree \\\\ \implies \sf\angle P = 60 \degree$

Thus angle P is 60°

Now using the trigonometric function sin to determine angle Q

$\sf \sin R = \dfrac{PQ}{PR} \\ \\ \implies \sf \sin R = \frac{3cm}{6cm} \\\\ \implies \sf \sin R = \dfrac{1}{2} \\\\ \implies \sf\sin R = \sin30 \degree \\ \\ \implies \sf \angle R = 30 \degree$

Thus angle R is 30°