In the diagram, is parallel to. Also, is drawn such that the length of is half the length of. If sin A = 0.5, then what is sin E

Question

seraphim [82]

2 years ago

15

In the diagram, is parallel to. Also, is drawn such that the length of is half the length of. If sin A = 0.5, then what is sin E

?

Mathematics

1 answer:

Tema [17] · Answer 1 · 2023-09-05T09:16:02+03:00

sinE is 0.5

What are similar triangles?

Two triangles will be similar if the angles are equal (corresponding angles), and sides are in the same ratio or proportion (corresponding sides). Similar triangles may have different individual lengths of the sides of triangles, but their angles must be equal and their corresponding ratio of the length of the sides must be the same.

Clearly, given triangle AFB and triangle DFE are similar.

We know that Similar Triangles have the same corresponding angle

We can find sinE as show below:

From diagram clearly

∠A=∠E

and ∠B=∠D

Since, ∠A=∠E

Taking sin on both sides

sinA=sinE

Give, sinA=0.5

sinA=sinE=0.5

⇒ sinE=0.5