Use the formula to find the length of the base next to the goal given that the height of the trapezoid is 11ft and the base farthest from the goal is 28ft

b1 = 22 ft

the length of the base next to the goal is 22 ft

Step-by-step explanation:

From the given formula;

Area A = 1/2×(b1 + b2)h ........1

Given;

Area A = 275ft^2

base b2 = 28 ft

base b1 = ?

height h = 11 ft

From equation 1;

Making b1 rhe subject of formula;

A = 1/2×(b1 + b2)h

Multiply through by 2;

2A = (b1+b2)h

b1+b2 = 2A/h

b1 = 2A/h - b2 ...... 2

Substituting the given values into equation 2;

b1 = 2(275)/11 - 28

b1 = 50 - 28

b1 = 22 ft

the length of the base next to the goal is 22 ft

answer: (3,11) is your answer.

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9