Ben thinks that the slope ratio for this triangle is 7/10. Carlissa thinks the ratio is 10/7 Who is correct? Explain your thinki
ng fully.
1 answer:
Answer:
Both answers are correct, depending on the angle taken as reference
Step-by-step explanation:
we know that
In a right triangle
The slope ratio of the triangle is equal to the function tangent
The function tangent in a right triangle is equal to the opposite side to the angle divided by the adjacent side to the angle
so
-----> Ben's ratio
and
------> Carlissa's ratio
therefore
The slope will depend on the angle taken as a reference
so
Both answers are correct, depending on the angle taken as reference.
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Answer:
Given A triangle ABC in which
∠C =90°,∠A=20° and CD ⊥ AB.
In Δ ABC
⇒∠A + ∠B +∠C=180° [ Angle sum property of triangle]
⇒20° + ∠B + 90°=180°
⇒∠B+110° =180°
∠B =180° -110°
∠B = 70°
In Δ B DC
∠BDC =90°,∠B =70°,∠BC D=?
∠BDC +,∠B+∠BC D=180°[ angle sum property of triangle]
90° + 70°+∠BC D =180°
∠BC D=180°- 160°
∠BC D = 20°
In Δ AC D
∠A=20°, ∠ADC=90°,∠AC D=?
∠A + ∠ADC +∠AC D=180° [angle sum property of triangle]
20°+90°+∠AC D=180°
110° +∠AC D=180°
∠AC D=180°-110°
∠AC D=70°
So solution are, ∠AC D=70°,∠ BC D=20°,∠DB C=70°
