What is the length of segment DF? B
4/28
1
68°
C
2
А A
2
3
8
4
68°
28°
F
5
Type your answer.

DF = 17.12

Step-by-step explanation:

From the picture attached,

From ΔABC and ΔEFD,

m∠ABC = m∠EFD = 28°

m∠BAC = m∠EDF = 68°

By AA property of similarity, ΔABC and ΔEFD will be similar.

And their corresponding sides will be proportional.

EF = 16

Now by applying cosine rule in ΔDEF,

DF² = ED² + EF² - 2(ED)(EF)cos(E)

DF² = 8² + (16)² - 2(8)(16)cos(84)°

DF² = 320 - 26.76

DF = √(293.24)

DF = 17.12

In a right triangle, one angle should be a right angle, which means that angle should be 90°. Right angles are always 90°.

And in any triangle, the sum of the 3 interior angles should add up to 180°, this rule is always the same. Therefore, to find the third angle, we should simply subtract the angles we already know from the angle sum of triangle.

We can therefore list this equation:
Third angle = 180° - 24° - 90°
Third angle = 66°

Your answer should be 66°