What is the value of x?

Mathematics

2 answers:

Anestetic [448]2 years ago

6 0

They are congruent triangles,

Ratio of their corresponding sides is 5:25, =1:5 (look for hypotenuse)

so, 5x = 18-x (same manner for variable one)

18 = 6x

x=3

SO, OPTION C IS THE ANSWER.

Zolol [24]2 years ago

3 0

Congruent triangles so therefor teh ratio are the same

5/x=25/(18-x)
multily both sies by (x(18-x))
5(18-x)=25x
90-5x=25x
add 5x to both sides
90=30x
divide both sides by 30
3=x
C is answer

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If x is a positive acute angle and cos x = 3/5, find the value of sinx.

Dima020 [189]

X is a positive acute angle. That means x is located in the first quadrant and has positive value in sin, cos, tan.

The formula of trigonometry ratio
cos x = $\dfrac{\text{adjacent}}{\text{hypotenuse}}$
sin x = $\dfrac{\text{opposite}}{\text{hypotenuse}}$

From the formula of cosine
cos x = $\dfrac{3}{5}$
$\dfrac{\text{adjacent}}{\text{hypotenuse}}= \dfrac{3}{5}$
from the formula above, adjacent side is 3 units, and hypotenuse is 5 units

Draw a right triangle to illustrate the location of the sides. See image attached.

To find the ratio of sine, we need to find the length of opposite side using pythagorean theorem
3² + (opposite)² = 5²
9 + (opposite)² = 25
(opposite)² = 25 - 9
(opposite)² = 16
opposite = 4
The length of opposite side is 4 units

Find sin x
sin x = $\dfrac{\text{opposite}}{\text{hypotenuse}}$
sin x = $\dfrac{4}{5}$