Use the diagram to answer the question. What is the measure of ∠A? Enter the correct value. Do not enter the degree symbol.
1 answer:
Answer:
Measure of ∠A = 60.07°
Step-by-step explanation:
From the figure attached,
ΔABC is a right triangle,
Measure of side AC = 15 units
and measure of side BC = 13 units
By applying Sine rule in this triangle,
SinA =
Opposite side of angle A = Side AC
and hypotenuse of the triangle = Side BC
SinA =
A =
A = 60.07°
Therefore, measure of angle A is 60.07°.
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Answer:
The angles are 45°, 60° , 75°
Step-by-step explanation:
<h3>Angle sum property:</h3>Sum of all the angles of a triangle is 180°.
Equation:
3x + 5x + 4x = 180
Combine like terms,
12x = 180
x = 180/12
3x = 3 *15 = 45°
5x = 5* 15 = 75°
4x = 4 *15 = 60°
Answer:
(A) Set A is linearly independent and spans . Set is a basis for
.
Step-by-Step Explanation
<u>Definition (Linear Independence)</u>
A set of vectors is said to be linearly independent if at least one of the vectors can be written as a linear combination of the others. The identity matrix is linearly independent.
<u>Definition (Span of a Set of Vectors)</u>
The Span of a set of vectors is the set of all linear combinations of the vectors.
<u>Definition (A Basis of a Subspace).</u>
A subset B of a vector space V is called a basis if: (1)B is linearly independent, and; (2) B is a spanning set of V.
Given the set of vectors , we are to decide which of the given statements is true:
In Matrix , the circled numbers are the pivots. There are 3 pivots in this case. By the theorem that The Row Rank=Column Rank of a Matrix, the column rank of A is 3. Thus there are 3 linearly independent columns of A and one linearly dependent column.
has a dimension of 3, thus any 3 linearly independent vectors will span it. We conclude thus that the columns of A spans
.
Therefore Set A is linearly independent and spans . Thus it is basis for
.