Answer:
62.4 ft²
Step-by-step explanation:
The unmarked horizontal dimension at the bottom of the triangle is ...
(8 ft)sin(30°) = 4 ft
The unmarked vertical dimension of the triangle (the height of the trapezoid) is ...
(8 ft)cos(30°) ≈ 6.93 ft
Then the area of the trapezoid is given by the formula ...
A = (1/2)(b1 +b2)h
A = (1/2)((4 ft+7 ft) +(7 ft))(6.93 ft) ≈ 62.4 ft²
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The mnemonic SOH CAH TOA can remind you of the relationships between right triangle dimensions and angles.
Sin = Opposite/Hypotenuse ⇒ Hypotenuse×Sin = Opposite
Cos = Adjacent/Hypotenuse ⇒ Hypotenuse×Cos = Adjacent
using pythagorean theorem
a^2 + b^2 =c^2
a^2 +8^2 =14^2
a^2 +64 = 196
subtract 64 from each side
a^2 = 132
take the square root of each side
a^2 = sqrt (132)
a=11.48912529
a =11.5
Check the picture below.
notice, it simply got mirrored over the vertical y-axis.
64 is written as 3√64=4. The 3rd root of -64, or -64 radical 3, or the cube root of -64 is written as 3√−64=−4. The cube root of 8 is written as 3√8=2.
