Question

ΔTRY is a right-angled isosceles triangle then cos T + cos R + cos Y is _____

Answer 1

Answer:

hey mate root 2 is the right answer

hope it was helpful for you

Answer 2

The value of cos T + cos R + cos Y is √2.

Given: ΔTRY is a right-angled isosceles triangle.

To find: We have to find cos T + cos R + cos Y.

Solution:

An isosceles right-angled triangle has two equal sides and one 90° angle.

Let angle R is 90°.

TR and RY are two equal sides.

The sum of three angles is 180°.

Thus we can write-

TRY+RYT+RTY=180°

TRY is 90°.

RYT=RTY

Let angle RYT is x.

$2x + 90 = 180 \\ 2x = 90 \\ x = 45$

Value of cos T + cos R + cos Y will be-

$cos90 + cos45 + cos45 \\ = 0 + \frac{1}{ \sqrt{2} } + \frac{1}{ \sqrt{2} } \\ \frac{2}{ \sqrt{2} } \\ = \sqrt{2}$

The value of cos T + cos R + cos Y is √2.