Two construction workers, Tyrone and Diego, are standing 15 yards apart, looking up at a piano hanging between the two men from
a crane. Tyrone is staring at the piano with an angle of elevation of 65°, and Diego is looking up with an angle of elevation of 77°. What is the distance between Tyrone and the piano? Round the answer to the nearest tenth.
1 answer:
Answer:
The distance between Tyrone and the piano is 23.7 yards
Step-by-step explanation:
see the attached figure to better understand the problem
step 1
Find the measure of angle P
Remember that the sum of the internal angles of a triangle must be equal to 180 degrees
∠T+∠D+∠P=180°
substitute the given values
65°+77°+∠P=180°
142°+∠P=180°
∠P=180°-142°=38°
step 2
applying the law of sines
substitute the given values
therefore
The distance between Tyrone and the piano is 23.7 yards
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Answer and Step-by-step explanation: Scaterplot is a type of graphic which shows the relationship between to variables. In this question, you want to determine if there is a linear relationship between overhead widths of seals and the weights. So, the hypothesis are:
H₀: no linear correlation;
H₁: there is linear correlation;
In this hypothesis test, to reject H₀, the correlation coefficient r of the data set has to be bigger than the critical value from the table.
With α = 0.05 and n = 6, the critical value is 0.811.
The linear correlation is calculated as:
r = n∑xy - ∑x.∑y / √[n∑x² - (∑x)²] [n∑y² - (∑y)²]
r =
r = 0.9485
Since r is bigger than the critical value, H₀ is rejected, which means there is enough evidence to conclude that there is linear correlation between overhead widths and the weights.
In the attachments is the scaterplot of the measurements, also showing the relationship.
