What is the measure of angle A to the nearest degree?
1 answer:
There are several ways to find the angle at A.
One is to realize the bisector of angle A will make a right angle with BC, creating two congruent triangles with short leg 2 and hypotenuse 7. Then the sine of the half-angle at A will be 2/7, so
A = 2*arcsin(2/7)
A ≈ 2*16.6015° = 33.203°
The measure of the angle at A to the nearest degree is
33°
_____
Another way to find the angle is to use the Law of Cosines. After solving for the angle (A) in terms of sides a, b, c, you find
A = arccos((b²+c²-a²)/(2bc)) = arccos(7²+7²-4²)/(2*7*7))
A = arccos(82/98) ≈ 33°
And you can always use a triangle solver application.
One is to realize the bisector of angle A will make a right angle with BC, creating two congruent triangles with short leg 2 and hypotenuse 7. Then the sine of the half-angle at A will be 2/7, so
A = 2*arcsin(2/7)
A ≈ 2*16.6015° = 33.203°
The measure of the angle at A to the nearest degree is
33°
_____
Another way to find the angle is to use the Law of Cosines. After solving for the angle (A) in terms of sides a, b, c, you find
A = arccos((b²+c²-a²)/(2bc)) = arccos(7²+7²-4²)/(2*7*7))
A = arccos(82/98) ≈ 33°
And you can always use a triangle solver application.
You might be interested in
Answer:
(b) 1.95
Step-by-step explanation:
One of the easiest ways to evaluate an arithmetic expression of almost any kind is to type it into an on-line calculator. Many times, typing it into a search box is equivalent.
<h3>Application</h3>See the attachment for the search box input (at top) and the result. This calculator has the benefit that it <em>always follows the Order of Operations</em> when evaluating an expression. (Not all calculators do.)
ln(7) ≈ 1.95
__
<em>Additional comment</em>
If your math course is asking you to evaluate such expressions, you have probably been provided a calculator to use, or given the requirements for a calculator suitable for use in the course.
There are some very nice calculator apps for phone and tablet. Many phones and tablets already come with built-in calculator apps. For the purpose here, you need a "scientific" or "graphing" calculator. A 4-function calculator will not do.
As with any tool, it is always a good idea to read the manual for your calculator and work through any example problems.
__
Years ago, handheld calculators were not available, and most desktop calculators were only capable of the basic four arithmetic functions. Finding a logarithm required use of a table of logarithms. Such tables were published in mathematical handbooks, and extracts of those often appeared as appendices in math textbooks used in school.
