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Answer:
The value of x in centimeters is 22.5 cm
Step-by-step explanation:
The corresponding sides of the similar triangles are proportion which means have equal ratios
∵ Δ ABC is similar to Δ FGH
∵ AB and FG are corresponding sides
∵ BC and GH are corresponding sides
∵ AC and FH are corresponding sides
→ That means the ratios between them are equal
∴ =
=
∵ AB = 6 cm and FG = 15 cm
∵ BC = 5 cm and GH = 12.5 cm
∵ AC = 9 cm and FH = x
→ Substitute them in the rule above to find x
∴ =
=
→ By using cross multiplication with the 1st and 3rd ratios
∵ 6 × x = 15 × 9
∴ 6x = 135
→ Divide both sides by 6 to find x
∵ =
∴ x = 22.5 cm
∴ The value of x in centimeters is 22.5 cm
Answer:
Measure of the acute angle = 84°
Step-by-step explanation:
In the figure attached,
ABDE is a swimming pool having length 'AB' = 65 feet
Depth of one end of the pool is BE = 4 feet
And depth of the other end AD = 11 feet
Acute angle between the bottom of the pool (DE) and wall of the deep end (AD) is ∠ADE.
Now from ΔCDE,
tanx =
tanx =
x =
x = 6.15°
Now measure of acute angle the bottom of the pool makes with wall at he deep end,
m∠ADE = (90 - 6.15)°
= 83.85°
≈ 84°
