Question

9. In a right triangle , one side other than the hypotenuse is 8 cm and an acute angle is 45°. What is the length of the hypotenus?​

Answer 1

Answer:

8√2 cm

Step-by-step explanation:

Since we need to find a relation between an angle and two sides of a right angled triangle, we use trigonometry

We can consider the given side as either an adjacent side or the opposite side

Method: i Taking given side as adjacent side

Cos∅= Adjacent Side/ Hypotenuse

Cos 45° = 8/Hypotenuse

1/√2 = 8/Hypotenuse

Hypotenuse = 8√2 Cm

Method: ii Taking given side as opposite side

Sin45° = Opposite Side/Hypotenuse

1/√2 = 8/Hypotenuse

Hypotenuse = 8√2 cm

Hence, If an angle and a side is given of a right angled triangle, its all other sides can be determined using different trigonometric ratios

Answer 2

Answer:

$8 \sqrt{2}$

Step-by-step explanation:

See. If it is a right angles triangle then it is already stated 2 angles... That is 90° and 45°..Now u can find the 3rd angle as

180°-(90°+45°) = 45°

Now it becomes an iscoceles right angled triangle, so two sides other than the hypotenuse are equal. This means that the sides are 8cm.

Now,

$\sqrt({8}^{2} + {8}^{2})= \sqrt{64 + 64} = \sqrt{128} = 8 \sqrt{2}$

Hence, Your you got your answer.