2. from the top of a vertical cliff 40 m high, the object is 59.3m from the base of the cliff. find the angle of depression to the objeci. a) 34° b ) 940 c ) 104 degrees d) 540

is the angle of depression from the vertical cliff.

Option: A

Step-by-step explanation:

Given that, Height of the cliff (opposite side) = 40m

Distance of object from the base of the cliff (adjecent side)  = 59.3m

To find the angle of depression of the object. From trigonometric rule in a right angled triangle, we know that Angle of depression = Therefore, the angle of depression to the object is .

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;

answer:   28.56 feet (approx)

step-by-step explanation:

since, triangle abc has measure of angle c equal to 55 degrees, measure of angle abc equal to 90 degrees, and length of bc equal to 20 feet.

we have to find out the measurement of segment ab.

therefore, tan 55° =

but bc = 20 feet.

⇒ tan 55 ° =  

⇒ ab = 20 × tan 55 °

⇒ ab = 20 × 1.42814800674

⇒ ab = 28.5629601348   ≈ 28.56 feet