Question

In ΔABC, m∠A = 90°, m∠C = 20°, BC ≈ 12 cm, and AB ≈ 4.1 cm. Also, ΔABC ∼ ΔDEF and EF = 6 cm. Use this information for Items 1–6. Round to the nearest tenth of a unit if necessary.

Answer 1

Answer:

Angle F = m∠C = 20°

Angle E = m∠B = 70°

AC = 11.3 cm

DF = 5.6 cm

DE = 2.0 cm

Explanation:

the triangle is right angle triangle

 I \C

20

 I    \

 I   \12 cm

 I           \

AI_4.1cm__\B the triangle is right angle triangle

 I \F

 I    \

 I   \6cm

 I           \

DI_______\E

AC will be calculated by using pythagorean theorem

AC ^2 = BC^2 - AB^2

AC^2 = 127.19

AC = 11.3 cm

To calculate DF, we will use similarity method

AC/BC = DF/EF

11.3/12 = DF/6

DF = 5.6 cm

We will use the same similarity method to calculate DE

AC/AB = DF/DE

11.3/4.1 = 5.6/DE

DE = 2.0 cm

m∠B = 90 - 20 = 70

Therefore m∠B = 70°

m∠E = 70°, same as m∠B = 70°

Angle F = m∠C = 20°