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# Class Note for MATH 1330 at UH

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This 5 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 31 views.

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Date Created: 02/06/15

Math 1330 Section 72 Area of a Triangle In this section we ll use a familiar formula and a new formula to find the area of a triangle You have probably used the formula K bh to find the area of a triangle where b is the length of the base of the triangle and h is the height of the triangle We ll use this formula in some of the examples here but we may have to find either the base or the height using trig functions before proceeding Here s another approach to finding area of a triangle Consider this triangle Draw an altitude from C to AB to form two right triangles c Now that we have right triangles in the picture we can use a trigonometric functions to relate b h and angle A In the smaller triangle b is the hypoteneuse and h is the side opposite angle A so we can define sine of angleA as follows sinA Solving this equation for h we ll have h bsinA Using the familiar formula for area of the whole triangle we have K ch Substituting b sinA for h we have K bc sin A It is helpful to think of this as Area 12 side side sine of the included angle Example 1 Find the exact area of the triangle 14 k Example 2 Find the exact area of the triangle L Example 3 Find the area of the triangle Round t0 the nearest hundredth 12 L Example 4 Find the exact area of the triangle 12 135 19 Example 5 Find the area of the triangle Round to the nearest hundredth 21 Example 6 Find the area of an isosceles triangle with legs measuring 15 inches and base angles measuring 42 degrees each Round to the nearest hundredth Example 7 Find the area of APQR if 4Q 128 p 12 and r 15 Round to the nearest hundredth Example 8 Find the area of AXYZ if AX 63 AY 49quot z 22 and x 19 Round to the nearest hundredth Example 9 Ifthe area of ADEF is 366 with d 3 and e 9 nd all possible measures for angle F Round answers to the nearest degree Example 10 A regular hexagon is inscribed in a circle of radius 14 Find the exact area of the hexagon You can also nd the area of a segment of a circle The shaded area of the picture is an example ofa segment of a circle To nd the area of a segment nd the area of the sector with central angle 9 and radius OA Then nd the area of AOAB Then subtract the area of the triangle from the area of the sector Example 11 Find the area of the segment of the circle with radius 6 and central angle 57f measurlng Round the answer to the nearest hundredth

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