Trigonometry Question Full Solution

Question

Resha is planting a triangular garden. She wants to put a fence around it. The length of one side of the garden is 10 meters. If the angles at each end of this side are 440 degrees and 580 degrees, find the length of the fence needed to enclose the garden.

Include a diagram with your solution.

Answer 1

if you meant 44 and 58, not 440 and 580 then

use law of sines

a/siin44 = 10/sin78

b/sin58 = 10/sin78

a= side opposite 44 is about 7.1

b= side opposite 58 is about 8.67

sum of all 3 sides is about 10+7.1+8.67

= about 25.77 meters for the fence

Answer 2

Step 1: Find the missing angle.

Step 2: Using the Law of Sines, find the length of the remaining sides.

Step 3: Add up the side lengths to get the perimeter (aka length of fence needed).

P.S. - I'm assuming that you did not know how to type the degree symbol (°). No worries! On Windows hold down Alt and type 0176 on the number pad. Or you can do an online search for "degree symbol copy and paste" to grab it. ;-)

Answer 3

a = 10 m; angle A = 180° - (44° + 58°) = 78°; B = 44° and C = 58°.

By sin law b/sinB = a/sinA; b = asinB/sinA, c = asinC/sinA

Perimetr p = a(1 + sinB/sinA + sinC/sinA) = 10(1 + sin44°/sin78° + sin58°/sin78°) = 25.77 m

Answer 4