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## Resolved Question

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A building lot in a city is shaped as a 30° -60° -90° triangle. The side opposite the 30° angle measures 41 feet.

a. Find the length of the side of the lot opposite the 60° angle.

b. Find the length of the hypotenuse of the triangular lot.

c. Find the sine, cosine, and tangent of the 30° angle in the lot. Write your answers as decimals rounded to four decimal places.
by يا حسين
Member since:
March 09, 2012
Total points:
2,421 (Level 3)

## Best Answer - Chosen by Voters

a. The side opposite the 60° is 71.0141 feet

b. The hypotenuse is 82 feet

c. sin(30)=0.5000

cos(30)=0.8660

tan(30)=0.5773

I would also like to tell you something about 30,60,90 triangles. The side opposite the 90° angle, the hypotenuse, will always be double that of the side opposite the 30° angle. This is one of the reasons why this type of triangle (30,60,90) is considered a special triangle.
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• Member since:
January 07, 2006
Total points:
31,433 (Level 7)
30-60-90 is a triangle that is 1/2 of equilateral triangle
since latter has EQUAL SIDES, 30-60-90 has sides of 1, 2, and sqrt 3
with the 1 being the side of the equilateral that was bisected (cut in half), also making one 60 degree angle into 30 degrees. 2 is a hypotenuse, opposite the 90 degree angle, 1 is opposite the 30 degree angle, sqrt 3 is opposite the 60 degree angle -- last gives answer for (a) which is sqrt 3 times 41 ft

(b) answer is 2 times 41 ft

sine 30 deg = 1/2 or 41/82 ft thus 0.5000
cos 30 deg = this also left for you
tan 30 deg = 1/(sqrt 3) or 41 ft / (sqrt 3 x 41 ft) = you compute this

### Source(s):

1, sqrt 3 and 2 is ratio of sides that applies to 30-60-90 triangle
• by CDA
Member since:
December 15, 2008
Total points:
16,868 (Level 6)
Right-angled triangle with angles 30, 60, 90 degrees.
I presume you know what sines and cosines are.
If side opposite the 30 deg is 41 feet the hypotenuse is 82 feet since sin30 = 0.5 exactly.
The other side is 41sqrt3 feet, since sin60 = 1/2. sqrt3

From any trig tables you can find sin30, cos30, tan30 yourself, to 4 decimals, 5 decimals or more.
Or you can use a calculator, or even google.
• by Pranil
Member since:
March 02, 2007
Total points:
97,370 (Level 7)
The side opposite the 30° angle measures 41 feet.
The side opposite the 30° angle is 1/2 the measure of hypotenuse = 41 feet.
b) so hypotenuse = 41 × 2 = 82 feet

a) side opposite to 60° is √3/2 × hypotenuse
= √3/2 × 82 = 41√3

so sides are
41, 41√3 and 82
sin 30 = 41/82 = 1/2 = 0.5000
cos 30 = 41√3/82 = √3/2 = 0.8660
tan 30 = sin 30/cos 30
= 1/2 ÷ √3/2 = 1/√3 = 0.5774
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• by Roger
Member since:
August 01, 2009
Total points:
57,853 (Level 7)
a) 41(tan 60°) 41(√3) = 71.01 feet
b) the hypotenuse is 2 x41 = 82 feet
c) sin 30° = 0.5000
cos 30° = (√3)/2 = 0.8660
tan 30° = 1/(√3) = 0.5774