Round the following to the nearest degree:
42 \degree 24\rq
49 \degree 55\rq
99 \degree 40\rq
108 \degree 29\rq
Round the following to the nearest minute:
40\degree 18\rq 6\rq\rq
31\degree 23\rq 40\rq\rq
80\degree 23\rq 10\rq\rq
92\degree 50\rq 35\rq\rq
Convert the following as indicated:
82\degree 30\rq 37\rq\rq to degrees, correct to two decimal places.
45.5\degree to degrees and minutes
38.38 \degree to degrees, minutes and seconds.
Find the value of each of the following:
71 \degree 39\rq + 42 \degree 12\rq
23 \degree 51 \rq + 11 \degree 17\rq
64 \degree 51\rq - 54 \degree 17\rq
83 \degree 22 \rq - 27 \degree 38 \rq
111 \degree 18 ' - 49 \degree 46 '
90\degree - 13\degree 36\rq 42\rq\rq
90\degree - 69\degree 39\rq 22\rq\rq
85 \degree 29' 43''- 56 \degree 13' 18''
For each of the following, find the acute angle \theta, rounded to the nearest minute:
\sin \theta = 0.3168
\tan \theta = 2.897
\cos \theta = 0.8267
\tan \theta = 3.749
Consider the following triangle:
Evaluate \theta, rounding your answer to the nearest minute.
Find the value of the pronumeral in the following triangles, correct to two decimal places:
For the following triangles, find the angle \theta to the nearest minute.
Consider the following triangle. Find the value of x:
In degrees, correct to two decimal places.
To the nearest minute.
For the following triangles, find the value of x:
Correct to four decimal places.
To the nearest second.
During a particular time of the day, a tree casts a shadow of length 24\text{ m}. The height of the tree is estimated to be 7\text{ m}. Find the angle \theta, formed by the length of the shadow and the arm extending from the edge of the shadow to the height of the tree. Round your answer to two decimal places.
During rare parts of Mercury and Venus' orbit, the angle from the Sun to Mercury to Venus is a right angle, as shown in the diagram. The distance from Mercury to the Sun is 60\,000\,000\text{ km}. The distance from Venus to the Sun is 115\,000\,000\text{ km}. What is the angle, \theta, from Venus to the Sun to Mercury? Round your answer to the nearest minute.
A fighter jet, flying at an altitude of 2000 \text{ m} is approaching an airport. The pilot measures the angle of depression to the airport to be 13 \degree. One minute later, the pilot measures the angle of depression again and finds it to be 16 \degree.
Find the distance AC, to the nearest metre.
Find the distance BC, to the nearest metre.
Hence, find the distance covered by the jet in that one minute, to the nearest metre.
A safety fence is constructed to protect tourists from the danger of an eroding castle toppling down. The surveyor takes an angle measurement to the top of the tower of 10 \degree. She then walks 29 \text{ m} towards the tower and takes another reading of 22 \degree.
Find the value of h to the nearest metre.
