Question

$\huge \fbox \red{❥ Question}$

In triangle PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.​

Answer 1

Answer:

Step-by-step explanation:

Answer:-

Given:-

• A right angle triangle PQR, right angles at Q.
• PR+QR = 25 cm
• PQ = 5 cm

Concept:-

Trigonometry and its applications

Let's Do!

As we are given that PR+QR = 25 cm, we can write it as:-

PR = 25-QR --------------(1)

Now, we will apply Pythagoras Theorem,

$\rm{(Hyp)^2 = (Base)^2+(Height)^2}$

$\rm{(25-QR)^2 = 5^2 + QR^2}$

$\rm{625+QR^2-50QR = 5^2 + QR^2}$

$\rm{625 -50 \ QR = 25}$

$\rm{QR = 12 \ cm}$

Now, we can find RP easily!

$\rm{PR = 25 - 12}$

$\rm{PR = 13 \ cm}$

Now, we can find sinP, cosP and tanP.

We know that:-

$\boxed{\sf{sin \theta = \dfrac{Height}{Hypotenuse}}}$

$\boxed{\sf{cos \theta = \dfrac{Base}{Hypotenuse}}}$

$\boxed{\sf{tan \ \theta = \dfrac{sin \ \theta }{cos \ \theta} \ or \dfrac{Height}{Base} }}$

So, we have :-

• Base as QR and height as PQ.
• Hypotenuse as PR.

1. So, sin P = 12/13
2. And, cos P = 5/13
3. Tan P = 12/5

And hence, are the answers.