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Chapter 6: Problem 35

Find the area of the triangle having the given measurements. Round to the nearest square unit. $$B=36^{\circ}, a=3 \text { yards, } c=6 \text { yards }$$

Short Answer

Expert verified
The area of the triangle, rounded to the nearest square unit, is \(7\) square yards.

Step by step solution

01

Identify given values

Identify the given values in the equation. The measurements provided are: the angle \(B = 36^{\circ}\), side \(a = 3\) yards, side \(c = 6\) yards.
02

Convert the degree to radian

The sine function in calculators often requires the angle to be in radian form. Convert the given angle from degrees to radians. The conversion is done by multiplying the degree by \(\frac{\pi}{180}\). Therefore, to convert \(36^{\circ}\), you have to multiply it by \(\frac{\pi}{180}\) to get the radian form.
03

Use formula to calculate the area

Use the formula for the area of a triangle when two sides and their included angle are known, which is \(Area = 0.5 \times a \times c \times \sin(B)\). Substitute the given values into the formula and simplify to get the area.
04

Round off Area

The problem statement asks to round the area to the nearest whole number. Use standard rounding rules to round off your answer.

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