LAw of Cosine

The spinner of the compass is two congruent isosceles triangles connected by their bases as shown in the diagram. The base of each of these triangles is 2 centimeters and the legs are 5 centimeters. If the metal used to construct the spinner costs $13.25 per square centimeter, how much will it cost to make this part of the compass? Round to the nearest cent.

* $129.82

The triangle shown is an equilateral triangle. What is the area of the equilateral triangle with the length of each side equal to a?

* 1/2a*2 sine60

Triangle ABC is an equilateral triangle with side lengths labeled a, b, and c. Trigonometric area formula: Area = Which expressions represent the area of triangle ABC? Select three options.

* 1/2bc(sin 60) * 1/2 a*2(sin60) * ab(sin60) / 2

Trigonometric area formula: Area = 1/2 ab sineC The area of triangle EFG is 34.8 square units. What is the perimeter of triangle EFG to the nearest unit?

* 29 units

Marta is making a flag with the given dimensions. The perimeter of the flag is 100 inches. (18, 41, x) How much material, in square inches, is needed to make the flag? If the material costs $0.15 per square inch, how much will Marta spend on materials to make the flag?

* 360 sq in * $54

Lian is making a banner for the school gym. She cut three pieces of fabric into congruent isosceles triangles, as shown. Trigonometric area formula: Area = To the nearest square inch, how much fabric will she use to make all three triangles?

* 417 sq in

An equilateral triangle has a semiperimeter of 6 meters. What is the area of the triangle? Round to the nearest square meter.

* 7 sq m

A spinner for a board game consists of a cardboard circle with two plastic arrows anchored to its center. The arrows are congruent isosceles triangles connected at their bases, as shown. Heron's formula: Area = The base of each triangle measures 2 centimeters and the perimeter of each triangle is 10 centimeters. What is the approximate total area of the plastic triangles on the spinner?

* 7.7 cm

Which triangle's area would be calculated using the trigonometric area formula?

* PQR

What information relevant to calculating area do we have available for this triangle? Which method should we use to calculate the area for this triangle? What is the area of this triangle calculated to the nearest hundredth of a square unit? Triangle DEF, DE=12, ER=10, DF=7

* SSS * Herons formula * 34.98 square units

Which statement about the relative areas of ΔABC and ΔXYZ is true?

* The area of ΔABC > the area of ΔXYZ

Using Heron's formula, calculate the area of the parallelogram to the nearest tenth of a square unit. [5,8,11]

* area = 18.33(2) = 36.7

Consider the diagram and the derivation below. Given: In △ABC, AD ⊥ BC. Derive a formula for the area of △ABC using angle C. It is given that in △ABC, AD ⊥ BC. Using the definition of sine with angle C in △ACD results in sin(C) = . Using the multiplication property of equality to isolate h, the equation becomes bsin(C) = h. Knowing that the formula for the area of a triangle is A = bh is and using the side lengths as shown in the diagram, which expression represents the area of △ABC?

*1/2 ab sinc

Trigonometric area formula: Area = 1/2 ab(SinC) What is the area of triangle DEF? Round to the nearest tenth of a square unit.

*10.3 square units

The perimeter of triangle XYZ is 24 units. What is the area of triangle XYZ? Round to the nearest tenth of a square unit. Trigonometric area formula: Area=1/2ab(sinC)

*14.7 square units

What is the area of triangle ABC? Round to the nearest hundredth of a square unit. [AB=16; AC=12; CB=14]

*81.33 sq units

See the figure of ΔABC with auxiliary lines added. If c is the base of ΔABC, the height is ______________ sin(A) = ______ The previous statement is leading to the derivation of which area formula? Area ΔABC =

*CD *CD/b *1/2bcsinA

Which triangle's area can be calculated using the trigonometric area formula?

*D (sas)