(2/3)^x-1=27/8, Find x
2 answers:
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The relationship between the lengths of the sides of a right triangle are
given by Pythagoras theorem.
- Part A: <u>ΔABC is similar to ΔADC</u>
- Part B: ΔABC and ΔADC are similar according <u>AA similarity postulate</u>
- Part C: <u>DA = 6</u>
Reasons:
Part A:
∠A = 90°
Segment AD ⊥ Segment BC
Location of point D = Side BC
Part A: In triangle ΔABC, we have;
∠A = 90°, ∠B = 90° - ∠C
In triangle ΔADC, we have;
∠ADC = 90°, ∠DAC = 90° - ∠C
∴ <u>ΔABC is similar to ΔADC</u> by Angle-Angle, AA, Similarity Postulate
Part B: The triangles are similar according to <u>AA similarity postulate</u>,
because two angles in one triangle are equal to two angles in the other
triangle and therefore, by subtraction property of equality, the third angle
in both triangles are also equal.
Part C: The length of DB = 9
The length of DC = 4
Required: Length of segment DA
In triangle ΔABD, we have;
∠BDA = 90°= ∠ADC
∠DAC ≅ ∠B by Congruent Parts of Congruent Triangles are Congruent
Therefore;
ΔABD ~ ΔADC by AA similarity, which gives;
=
Which gives;
= 4 × 9 = 36
= √(36) = 6
<u> = 6</u>
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