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Goshia [24]
2 years ago
15

Find the length of the hypotenuse

Mathematics
1 answer:
Yakvenalex [24]2 years ago
5 0
The answer is 13 cm

a = height , b= base ,c = hypotenuse

a^2 + b ^2 = c ^2 ( theorem of Pythagoras)
(12cm)^2+ (5cm)^2 = hypotenuse
144cm^2 + 25 cm ^3 = hypotenuse
169cm^2 = hypotenuse
Square toot of 169cm ^2 = hypotenuse
Answer : 13 cm = hypotenuse
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Need help ASAP <br> questions in the pics i have sent
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Answer:

Step-by-step explanation:

Picture 1

In right triangle ABC,

Side AB is the opposite side of angle C.

Picture 2

In triangle MKL,

tan(∠M) = \frac{\text{Opposite side}}{\text{Adjacent side}}

             = \frac{KL}{KM}

             = \frac{15}{8}

Option (1) is the answer.

Picture 3

In ΔXYZ,

sin(∠Z) = \frac{\text{Opposite side}}{\text{Hypotenuse}}

            = \frac{XY}{XZ}

For the length of XY we will apply Pythagoras theorem in ΔXYZ,

XZ² = XY² + YZ²

XY² = XZ² - YZ²

      = (40)² - (32)²

XY = √576

     = 24

sin(Z) = \frac{24}{40}

sin(Z) = \frac{3}{5}

Picture 4

In right triangle DEF,

Cos(D) = \frac{\text{Adjacent side}}{\text{Hypotenuse}}

           = \frac{EF}{DF}

           = \frac{75}{72}

           = \frac{25}{24}

Picture 5

In ΔABC,

tan(63°) = \frac{\text{Opposite side}}{\text{Adjacent side}}

tan(63°) = \frac{BC}{AB}

AB = \frac{BC}{\text{tan}(63)}

AB = \frac{8}{\text{tan}(63)}

AB = 4.0762 ≈ 4 m

Option (3) will be the answer.

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