Find the size of obtuse angle x for the following triangles, correct to two decimal places:
Find the size of the obtuse angle \theta, rounded to the nearest minute:
A line joining the origin and the point \left(6, 8\right) has been graphed on the number plane. To form a triangle with the x-axis, a second line is drawn from the point \left(6, 8\right) to the positive side of the x-axis.
In what interval can the length of the second line be such that there are two possible triangles that can be formed with that length?
What can the length of the second line be such that there is exactly one triangle that can be formed with that length?
For what lengths of the second line will no triangle be formed?
Rochelle needs to determine whether a triangle with the dimensions shown below is possible or not:
Find the value of \theta.
Find the value of \dfrac{8.4}{\sin 106 \degree}. Round your answer to four decimal places.
Find the value of \dfrac{4.0}{\sin 26 \degree}. Round your answer correct to four decimal places.
Hence, is it possible to construct this triangle? Explain your answer.
\triangle ABC consists of angles A, B \text{ and }C which appear opposite sides a, b \text{ and }c respectively. Given the following, state whether solving \triangle ABC results in the ambiguous case:
If a, b and c are known.
If A, B and a are known.
If A, a and c are known.
If a, B and c are known.
Determine the number of possible triangles given the following:
a = 50, b = 58 and A = 60 \degree
a = 23, b = 21 and A = 35 \degree
B = 30 \degree, b = 4 and c = 8
a = 39, b = 32 and B = 50 \degree
Determine whether the following sets of data determine a unique triangle:
B = 40 \degree, b = 2, c = 5
a = 6, b = 3, c = 27
a = 3, b = 4, c = 5
a = 80 \degree, b = 20 \degree, c = 80 \degree
a = 5, b = 6, C = 80 \degree
A = 50 \degree, B = 30 \degree, c = 8
a = 20 \degree, b = 40 \degree, c = 120 \degree
a = 5, b = 12, c = 13
\angle CAB = 42 \degree, a = 7, b = 2
Consider \triangle ABC below:
Find x, given that x is acute. Round your answer to the nearest degree.
Find \angle ADB to the nearest degree, given that \angle ADB > x.
For each of the given measurements of \triangle ABC:
Determine whether such a triangle exists.
If so, state whether the triangle could be acute and/or obtuse.
\angle CAB = 36 \degree, a = 7 and b = 10
\angle CAB = 35 \degree, a = 5 and b = 11
\triangle ABC is such that \angle CAB = 32 \degree, a = 5 and b = 9.
Let the unknown angle opposite the length 9 \text{ cm} be x.
Consider the acute case, and find the size of angle x, to two decimal places.
Consider the obtuse case, and find the size of the obtuse angle x, to two decimal places.
In \triangle ABC, A = 45\degree and c = 5\text{ mm}.
What is the range of lengths, rounded to the nearest tenth where appropriate, for BC that lead to the ambiguous case where we don't know if the triangle formed is acute or obtuse?
