Question

Find all three side lengths to the nearest hundredth and allhree angle measures to the nearest degree.B(-2, 4), C(3, 3), DC-2, 3)

Answer 1

BC = 8.60, CD = 5.00, BD = 7.00

∠D = 90° , ∠C = 54° , ∠B = 36°

Step-by-step explanation:

B(-2, 4), C(3, 3), D(-2, 3)

To get the three side lengths, we would find the distance between them.

Distance formula:

`dis\tan ce\text{ = }\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}`
`\begin{gathered} x_1=-2,y_1=-4,x_2=3,y_2\text{ =3} \\ Distance\text{ BC = }\sqrt[]{(3-(-4))^2+(3-(-2))^2} \\ \text{Distance BC = }\sqrt[]{(3+4)^2+(3+2)^2}\text{ =}\sqrt[]{(7)^2+5^2\text{ }} \\ \text{Distance BC = }\sqrt[]{49+25}\text{ } \\ \text{Distance BC = }\sqrt[]{74}\text{ = 8}.60 \\ \text{Distance BC = 8.60 (nearest hundredth)} \end{gathered}`
`\begin{gathered} x_1=3,y_1=3,x_2=-2,y_2\text{ =3} \\ \text{Distance CD = }\sqrt[]{(3-3)^2+(-2-3)^2} \\ \text{Distance CD =}\sqrt[]{(0)^2+(-5)^2}\text{ =}\sqrt[]{0+25} \\ \text{Distance CD =}\sqrt[]{25} \\ \text{ Distance CD = 5.00 (nearest hundredth)} \end{gathered}`
`\begin{gathered} x_1=-2,y_1=-4,x_2=-2,y_2\text{ = 3} \\ \text{Distance BD = }\sqrt[]{(3-(-4))^2+(-2-\mleft(-2\mright))^2} \\ \text{Distance BD =}\sqrt[]{(3+4)^2+(-2+2)^2} \\ \text{Distance BD =}\sqrt[]{7^2+0^2}\text{ =}\sqrt[]{49} \\ \text{Distance BD = 7} \\ \text{Distance BD = 7.00 (nearest hundredth)} \end{gathered}`

From the diagram, we can see it is a right angled triangle.

∠D = 90°

To get angle C, we would apply the trigonometry: SOHCAHTOA

opposite = side opposite angle C = BD = 7

hypotenuse = BC = 8.60

sin C = opposite/hypotenuse

sin C = 7/8.6

sinC = 0.81395

C = arc sin (0.81395)

C = 54.48°

To the nearest degree = 54°

To get angle A:

angle B + angle D + angle C = 180° (sum of angles in a triangle)

angle B + 90 + 54 = 180

angle B + 144 = 180

angle B = 180 - 144

angle B = 36° (nearest degree)