Answer:
AB = 42.15 units
Step-by-step explanation:
In triangle ABD,
By applying Cosine rule in this triangle,
cos(30)°=
=
AD =
By applying tangent rule in ΔACD,
tan(44)° =
tan(44)° =
0.9657 =
0.9657 =
x =
x = 42.15
≈ 42.2 units
In the diagram below, AC and CB, AB and CD, and m(angle)A=33 degrees. Find M(angle)B
1 answer:
Answer:
15°.
Step-by-step explanation:
1. Angles ADC and CDB are supplementary, thus
m∠ADC+m∠CDB=180°.
Since m∠ADC=115°, you have that m∠CDB=180°-115°=65°.
2. Triangle BCD is isosceles triangle, because it has two congruent sides CB and CD. The base of this triangle is segment BD. Angles that are adjacent to the base of isosceles triangle are congruent, then
m∠CDB=m∠CBD=65°.
The sum of the measures of interior angles of triangle is 180°, therefore,
m∠CDB+m∠CBD+m∠BCD=180° and
m∠BCD=180°-65°-65°=50°.
3. Triangle ABC is isosceles, with base BC. Then
m∠ABC=m∠ACB.
From the previous you have that m∠ABC=65° (angle ABC is exactly angle CBD). So
m∠ACB=65°.
4. Angles BCD and DCA together form angle ACB. This gives you
m∠ACB=m∠ACD+m∠BCD,
m∠ACD=65°-50°=15°.
Have a good Day!
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Answer:
B
Step-by-step explanation:
Reflection is a transformation that preserves lengths.
Triangle XYZ, with side lengths XY = 7 in, YZ = 5 in, XZ = 4 in, is reflected across the x-axis to result in △X'Y'Z'.
This means that corresponding sides have the same lengths:
- XY = X'Y' = 7 in;
- XZ = X'Z' = 4 in;
- YZ = Y'Z' = 5 in.
Find the perimeters of both triangles:
Hence, only option B is true.