Find the value of x using the sine rule, noting that x is acute. Round your answer to two decimal places.
Consider the given \triangle ABC:
Find x, noting that x is acute. Round your answer to the nearest degree.
Find \angle ADB to the nearest whole degree, given that\angle ADB \gt \angle ACB.
The angle of depression from J to M is 71 \degree. The length of JK is 17\text{ m} and the length of MK is 19\text{ m}.
Find x, the size of \angle JMK, correct to two decimal places.
Find the angle of elevation from \\ M to K, correct to two decimal places.
For each of the following triangles, find the value of x correct to two decimal places, noting that x is obtuse:
Find the value of x correct to two decimal places, given that x is obtuse.
A line joining the origin and the point \left(6, 8\right) has been graphed on the number plane. To form a triangle, a second line is drawn from the point \left(6, 8\right) to the positive x-axis.
Consider the given lengths of the second line.
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Exactly 8
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Exactly 10
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Less than 8
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Greater than 10
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Between 8 and 10
Which lengths will form:
Two triangles
One triangle
No triangle
Consider the \triangle ABC with angles A, B and C which appear opposite sides a, b and c respectively.
Use the given options to determine the most appropriate statement that can be said about the triangles with the following measurements:
Option 1: The triangle must be a right-angled triangle.
Option 2: The triangle can be either acute or obtuse.
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Option 3: The triangle does not exist.
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Option 4: The triangle must be an obtuse triangle.
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Option 5: The triangle must be an acute triangle.
\angle CAB = 34 \degree, a = 6 and b = 10
\angle CAB = 22 \degree, a = 5 and b = 10
\angle CAB = 47 \degree, a = 6 and b = 10.
A line joining the origin and the point \left( - 8 , 6\right) has been graphed on the number plane. To form a triangle, a second line is drawn from the point \left( - 8 , 6\right) to the negative x-axis.
Consider the given lengths for the second line:
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Between 6 and 10
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Greater than 10
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Less than 6
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Less than 10
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Exactly 6
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Exactly 10
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There is no such line
Two triangles
One triangle
No triangle
Consider the \triangle ABC with angles A, B and C which appear opposite sides a, b and c respectively. Determine the number of possible triangles given:
a = 36, b = 35 and A = 34 \degree
a = 54, b = 70 and A = 55 \degree
B = 45 \degree, b = 2 \sqrt{2} and c = 4
a = 40, b = 34 and B = 44 \degree
Consider the \triangle ABC with angles A, B and C which appear opposite sides a, b and c respectively. Which set of data does not determine a unique triangle?
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Set A: A = 80 \degree, B = 20 \degree, c = 4
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Set B: A = 50 \degree, B = 30 \degree, C = 100 \degree
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Set C: a = 6, b = 7, C = 60 \degree
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Set D: a = 3, b = 4, c = 5
Consider the \triangle ABC with angles A, B and C which appear opposite sides a, b and c respectively. Which set of data determines a unique triangle?
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Set A: a = 4, b = 7, c = 22
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Set B: B = 60 \degree, b = 2, c = 5
Set C: a = 8, b = 15, c = 17
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Set D: a = 40 \degree, b = 80 \degree, c = 60 \degree
Consider the \triangle ABC with angles A, B and C which appear opposite sides a, b and c respectively, where \angle CAB = 53 \degree, a = 12 and b = 7.
Determine whether the following statements are true or false about the triangle:
There are two such triangles, one obtuse and one acute.
No such triangle exists.
Only one triangle exists
Consider the \triangle ABC with angles A, B and C which appear opposite sides a, b and c respectively, where \angle CAB = 32 \degree, a = 5 and b = 9. The triangle could be an obtuse or an acute triangle. Let the unknown angle opposite the side with length 9\text{ m} be x.
For the acute case, find the size of angle x, correct to two decimal places.
For the obtuse case, find the size of angle x, correct to two decimal places.
Consider the \triangle ABC with angles A, B and C which appear opposite sides a, b and c respectively. Determine whether each of the following could result in the ambiguous case:
b, a and c are known
A, C and a are known
B, b and a are known
Fiona needs to determine whether a triangle with certain dimensions is possible. A triangle is sketched out and the dimensions are added as shown below:
Find the size of the unknown angle \theta:
Use the sine rule to determine whether it is possible to construct this triangle.
Consider \triangle ABC where A=37\degree and c=14.2 \text{ m}:
Find the range of lengths, rounded to the nearest tenth where appropriate, for BC so that it results in two triangles. That is, what values of BC lead to the ambiguous case where we don't know if the triangle formed is acute or obtuse?