Question

in ∆PQR, if angle P is obtuse angle ,then


(need with explanation)​

Answer 1

Answer:

Correct option is

A

<90

o

If ΔPQR is a obtuse triangle with ∠Q as the obtuse angle, then the measure of ∠Q>90

o

and measure of ∠P and measure of ∠R is <90

o

.

This can be verified using angle sum property.

Step-by-step explanation:

Correct option is

A

<90

o

If ΔPQR is a obtuse triangle with ∠Q as the obtuse angle, then the measure of ∠Q>90

o

and measure of ∠P and measure of ∠R is <90

o

.

This can be verified using angle sum property.

Answer 2

Answer:

p² > q² + r²

Step-by-step explanation:

Assumption,

Let the length of the sides opposite to the angles P, Q, and R be p, q, and r.

Given,

Triangle PQR is an obtuse-angled triangle with P as its obtuse angle.

To find,

The relation between the sides p, q, and r.

Calculation,

We know that from the cosine rule:

$\cos(p) = \frac{q^2+r^2-p^2}{2qr}$

But p is greater than 90 degrees so:

cos(p) < 0

⇒ 2qr (cos(p)) < 0

But from equation (1)

q² + r² - p² < 0

⇒ p² > q² + r²

Therefore, the relation between the sides is p² > q² + r².

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