Question

Do question one please

Answer 1

A. w = 17.83 mm

B. b = 7.54 mm

C. a = 6.63 mm

D. c = 10.28 mm

Explanation:

A. a^2 + b^2 = c^2
13^2 + 12^2 = w^2
169 + 148.84 = w^2
square root of 317.84 = w

w = 17.83 mm

B. 6.1^2 + b^2 = 9.7^2
37.21 + b^2 = 94.09

b = square root of 94.09 - 37.21

b = 7.54 mm

C. a^2 + 3.5^2 = 7.5^2
a = square root of 56.25-12.25

a = 6.63 mm

D. c^2 + 9.5^2 = 14^2
c = square root of 196 - 90.25

c = 10.28 mm

Answer 2

a. w = 17.8 m

b. b = 7.5 mm

c. a = 6.6 mm

d. c = 10.3 mm

Explanation:

The Pythagorean theorem is a mathematical theorem that states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Formula:

`\sf a^2 + b^2 = c^2`

Where:

• a and b are the lengths of the two legs of the triangle
• c is the length of the hypotenuse

We can use these theorems to solve the problem given:

a.

`\begin{aligned} 13^2 + 12.2 ^2 &= w^2 \\\\ 317.84 &= w^2 \\\\ w &= √(317.84) \\\\ w &= 17.8 \textsf{m (in 1 d.p)} \end{aligned}`

b.

`\begin{aligned} 6.1 ^2 + b^2 &= 9.7^2 \\\\ b^2 &= 9.7^2 - 6.1^2 \\\\ b ^2 &= 56.88 \\\\ b &= √(56.88) \\\\ b&= 7.5 \textsf{ mm (in 1 d.p)} \end{aligned}`

c.

`\begin{aligned} a^2 + 3.5^2 &= 7.5^2 \\\\ a^2 &= 7.5^2 - 3.5^2 \\\\ a ^2 &= 44 \\\\ a &= √(44) \\\\ a&= 6.6 \textsf{ mm (in 1 d.p)} \end{aligned}`

d.

`\begin{aligned} 9.5 ^2 + c^2 &= 14^2 \\\\ c^2 &= 14^2 - 9.5^2 \\\\ c ^2 &= 105.75 \\\\ c&= √(105.75) \\\\ c&= 10.3 \textsf{ mm (in 1 d.p)} \end{aligned}`