Question

Could someone please help me

Answer 1

Answer:

1)  8 cm

2)  15 ft

3)  3√10 ft = 9.5 ft (nearest tenth)

Step-by-step explanation:

Pythagoras’ Theorem

$a^2+b^2=c^2$

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Question 1

Given:

• a = 6
• b = x
• c = 10

Substitute the given values into the equation and solve for x:

$\implies 6^2+x^2=10^2$

$\implies 36+x^2=100$

$\implies x^2=100-36$

$\implies x^2=64$

$\implies x=\sqrt{64}$

$\implies x=8\: \sf cm$

Question 2

Given:

• a = 9 ft
• b = 12 ft

Substitute the given values into the equation and solve for c:

$\implies 9^2+12^2=c^2$

$\implies 81+144=c^2$

$\implies c^2=225$

$\implies c=\sqrt{225}$

$\implies c=15\: \sf ft$

Question 3

Given:

• a = 3 ft
• b = 9 ft

Substitute the given values into the equation and solve for c:

$\implies 3^2+9^2=c^2$

$\implies 9+81=c^2$

$\implies c^2=90$

$\implies c=\sqrt{90}$

$\implies c=\sqrt{9 \cdot 10}$

$\implies c=\sqrt{9}\sqrt{10}$

$\implies c=3\sqrt{10}\: \sf ft$

Answer 2

The second attachment I solved in your another question.You may refer to that.

#1

Apply Pythagorean theorem

x²=10²-6²

• x²=100-36
• x²=64
• x=8cm