Question

Solve the given right triangle for its missing angle and side measures.

An Image of a Right triangle FED With E being the right angle and FE being the base with 12units. The acute angle is F at 35degree.

Note: Figure not drawn to scale

A.
m∠D = 35°, DE ≈ 8.40 units, DF ≈ 13.65 units
B.
m∠D = 35°, DE ≈ 8.40 units, DF ≈ 14.65 units
C.
m∠D = 55°, DE ≈ 4.40 units, DF ≈ 13.65 units
D.
m∠D = 55°, DE ≈ 8.40 units, DF ≈ 14.65 units

Answer 1

A m∠D = 55°, DE ≈ 8.40 units, DF ≈ 14.65 units

Explanation:

Answer 2

D

Explanation:

the sum of the 3 angles in Δ DEF = 180° , that is

∠ D + 90° + 35° = 180°

∠ D + 125° = 180° ( subtract 125° from both sides )

∠ D = 55°

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using the tangent and cosine ratios in the right triangle

tan35° =
`(opposite)/(adjacent)` =
`(DE)/(EF)` =
`(DE)/(12)` ( multiply both sides by 12 )

12 × tan35° = DE , then

DE ≈ 8.40 ( to 2 dec. places )

--------------------------

cos35° =
`(adjacent)/(hypotenuse)` =
`(EF)/(DF)` =
`(12)/(DF)` ( multiply both sides by DF )

DF × cos35° = 12 ( divide both sides by cos35° )

DF =
`(12)/(cos35)` ≈ 14.65 ( to 2 dec. places )