In ΔQRS, r = 510 cm, ∠S=5° and ∠Q=15°. Find the area of ΔQRS, to the nearest centimeter.

The area is 8,652 square centimeters (rounded off to the nearest centimeter)

Step-by-step explanation: The triangle has one side given and two angles given as well. The third angle can be calculated as follows;

Angle R = 180 - (5 + 15)

Angle R = 180 - 20

Angle R = 160

To calculate side s we shall apply the Sine rule.

s/SinS = r/SinR

s/Sin5 = 510/Sin160

By cross multiplication we now have

s = (510 x Sin5)/Sin160

s = (510 x 0.0872)/0.3420

s = 44.472/0.3420

s = 130

Next we calculate side q as follows;

q/SinQ = r/SinR

q/Sin15 = 510/Sin160

By cross multiplication we now have

q = (510 x Sin15)/Sin160

q = (510 x 0.2588)/0.3420

q = 131.988/0.3420

q = 385.929

q = 386 (approximately)

Having found all three sides of the triangle as 130, 386 and 510 respectively the area shall be calculated by use of the Heron’s formula which is;

A = [square root] s(s - a)(s - b)(s - c)

Where s is the semi-perimeter, a, b and c are the three sides. The semi-perimeter is calculated as follows;

s = (130 + 386 + 510)/2

s = 1026/2

s = 513

The area now becomes

A = [square root] 513(513 - 510)(513 - 386)(513 - 130)

A = [square root] 513(3)(127)(383)

A = [square root] 74858499

A = 8652.0806

Rounded to the nearest centimeter, the area of the triangle is 8,652 square centimeters.

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.