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1. DC is tangent to circle O at C. If ∠ABC = 59 degrees, ∠BAC = 60 degrees, and ∠BCA = 61 degrees, then what is the measure of ∠ACD?

2.  In acute  triangle ABC, AB = 3 and BC = 5. Find the number of possible integer values of CA.

3. One interior angle of a rhombus is 150 degrees. The area of the rhombus is 50 square meters. What is the perimeter of the rhombus in meters?

Mar 3, 2021

#2
+485
+1

1. 180-(90-60+90)=angle ACD=$\boxed{60}$

2.

3+5>CA

3+CA>5

5+CA>3

largest possibility for CA:7

smallest possibility for CA:3

total possibilities for CA: $\boxed{5}$

3.

l/2$\cdot$l=50

l^2=100

l=10

10$\cdot$4=$\boxed{40}$

Mar 3, 2021

#1
+118069
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3. One interior angle of a rhombus is 150 degrees. The area of the rhombus is 50 square meters. What is the perimeter of the rhombus in meters?

1/2  of  the  area =   25 m^2

We  can  solve  this  to   find  a side length, S

(1/2) S^2 sin (150)  =  25      multiply  both sides  by 2

S^2  * (1/2)  =  50         mult through by 2 again

S^2   =100

S =  10

The perimieter  is  4 * 10  =    40 m

Mar 3, 2021
#2
+485
+1

1. 180-(90-60+90)=angle ACD=$\boxed{60}$

2.

3+5>CA

3+CA>5

5+CA>3

largest possibility for CA:7

smallest possibility for CA:3

total possibilities for CA: $\boxed{5}$

3.

l/2$\cdot$l=50

l^2=100

l=10

10$\cdot$4=$\boxed{40}$

SparklingWater2 Mar 3, 2021
#3
0

1. DC is tangent to circle O at C. If ∠ABC = 59 degrees, ∠BAC = 60 degrees, and ∠BCA = 61 degrees, then what is the measure of ∠ACD?

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Important: The measure of angle ACD is equal to the measure of angle opposite side AC.

∠ACD = 59º

Mar 3, 2021