Question

A right triangle has the side lengths 8 15 17
use these lengths to find cos B, tan B, and sin B

A
I\
I \
15 I \ 17
I \
I \
---------
8

Answer 1

Answer:

cos B = 0.470 , tan B = 1.875 , sin B = 0.888

Given-

Here we have a right-angle triangle of a

height/ perpendicular of 15,

the base of 8 and

hypotenuse of 17

To find

cos B, tan B, sin B in a right angle triangle with base angle B

Solution -

we know that cos B = base / hypotenuse

therefore, cos B = 8/ 17 = 0.470

we know that tan B = perpendicular/base

therefore, tan B = 15/8 = 1.875

we know that sin B = perpendicular / hypotenuse

therefore, sin B = 15/17 = 0.888

hence, cos B=0.470, tan B = 1.875, sin B =0.888, by using right-angle triangle trigonometric formulas we got cos B, tan B, and sin B.

Answer 2

The values of CosB; tanB and sinB are respectively 0.8823; 0.533 and 0.4705

Given,

A right triangle has the side lengths 8, 15, 17

To Find,

Find the value of CosB; tanB and sinB

Solution,

We know the Pythagorean theorem in mathematics.

Pythagorean theorem, states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

The mathematical represent of this law is:

$(Hypotenuse)^{2} = (Base)^{2} + (Altitude)^{2}$

so, from the above picture of right angle

We consider that,

$(AC)^{2} = (BC)^{2} + (AB)^{2}$

[ where AC= Hypotenuse; BC= Base and AB= Altitude]

so, now we have to find the value of CosB; tanB and sinB

so,

$CosB= \frac{BC}{AC}\\CosB= \frac{15}{17}$

or, CosB= 0.8823

$tanB= \frac{AB}{BC} \\tanB= \frac{8}{15}$

or, tanB= 0.533

$sinB= \frac{AC}{AB} \\sinB= \frac{8}{17}$

or, sinB= 0.4705

Hence, the values of CosB; tanB and sinB are respectively 0.8823; 0.533 and 0.4705

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