Answer:
2 -
Step-by-step explanation:
Using the addition formula for tangent
tan(A - B) = and the exact values
tan45° = 1 , tan60° = , then
tan15° = tan(60 - 45)°
tan(60 - 45)°
=
=
Rationalise the denominator by multiplying numerator/ denominator by the conjugate of the denominator.
The conjugate of 1 + is 1 -
= ← expand numerator/denominator using FOIL
=
=
= +
= 2 -
The measures of the angles of Δ DEF are 36° , 72° , 72°
Step-by-step explanation:
The sum of the measures of the interior angles in any triangle is 180°
In Δ DEF
The ratio between the measures of its interior angles is 2 : 4 : 4
To find the measure of each angle
1. Find the sum of the ratio between the measures of its angles
2. Divide 180° by the sum of the ratio
3. Multiply the quotient by each ratio
∵ The ratio between the measures of the angles of Δ DEF = 2 : 4 : 4
∴ The sum of the ratio = 2 + 4 + 4 = 10
→ m∠D : m∠E : m∠F : sum of the ratio
→ 2 : 4 : 4 : 10
→ ? : ? : ? : 180°
Divide 180 by 10, then multiply the quotient by the components of
the ratio to find the measure of each angle
∵ m∠D =
∴ m∠D = 36°
∵ m∠E =
∴ m∠D = 72°
∵ m∠F =
∴ m∠F = 72°
The measures of the angles of Δ DEF are 36° , 72° , 72°
Learn more:
You can learn more about the ratio in brainly.com/question/2707032
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